I answered a question just the other day similar to this, if you'd like to read that one; there was a somewhat more lively discussion on that post than usual. I have also written other comments addressing the causes of the war and some of its effects.
To more specifically answer your question, the simple answer is that no, the causes of the conflict had not been resolved. However, there was a widespread popular belief among Britons and Americans that the war was pointless. It was, as Donald Hickey has argued, the least popular war in US history, and inspired a huge number of protests, peaceful as well as violent. On the British side, there was a sense that the war was needless, coming at a point when American help against Napoleon would have been welcomed, and on the whole the war itself was a tragedy. The Federalist party in the US had actually suggested that a way to resolve the conflicts that led to the war was to ally with Britain and declare war on Napoleon themselves, but there was little support for it.
Circling back to the causes and whether they were resolved, though, we should understand what they were. For Madison to resort to "the last resort of injured nations," he appealed to three elements of British policy that were harming the country, summarized from an earlier answer:
- Impressment. British cruisers have been in the continued practice of violating the American flag on the great high way of nations, and of seizing and carrying off persons sailing under it. He was describing the British practice of Impressment: the deliberate searching of neutral nations' vessels and plucking off British citizens and especially former Royal Navy sailors who had deserted. The US felt particularly targeted, and the seizure of American sailors to fight the British war was considered a heinous insult to American sovereignty. I go over more detail on one particularly aggravating episode in this post
- Trade rights. Pursuing their war against Napoleon, the British had made a habit of plundering American trade. Their "Orders in Council" forbade all trade to the European mainland apart from those trading at British ports. Madison expressed a popular sentiment when he claimed that our commerce has been plundered in every sea. The practice had, according to those who supported the war, wrecked the US economy.
- The "Indian Problem." ...Our attention is necessarily drawn to the warfare just renewed by the Savages, on one of our extensive frontiers; a warfare which is known to spare neither age nor sex, and to be distinguished by features peculiarly shocking to humanity. The US perceived a Native-led spiritual revitalization led by a former wastrel who had changed his name from Lalawethika or "The Loudmouth/Rattle" to Tenskwatawa or "The Open-Door," who was often referred to simply as "The Prophet," as a British-led conspiracy to ignite the frontier against the United States. Andrew Jackson voiced a popular theory that The Prophet as his charismatic brother Tecumseh as an engine set in motion by the British.
Impressment was very much still an issue to the United States at the time of the declaration of war. The Chesapeake Affair, which saw a British warship firing on the USS Chesapeake, killing almost twenty men, and boarding her to carry off four British deserters, was very fresh in the consciousness of the United States, and while the British were careful to only take men who were either British citizens or royal navy deserters, the sense in the states was that the British were targetting American vessels and American citizens on purpose. But, short of ending the process entirely, there was little they could do to appease American sentiment.
The Orders in Council are a different story, because they had been repealed prior to the war's declaration. The US had called for their repeal because, as a blanket blockade of the European coast and declaring neutral nations' trade with the French, they were considered not only counter to the notion of neutrality and good commerce, but also felt like they were unfairly targeting Americans, who had the largest trading fleet in the world at the time, and who had traded with France for a long time. The US had also fought two smaller actions in the name of protecting the rights of neutral shipping: the Quasi-War under Adams in 1798, and the first Barbary War under Jefferson in 1801-5.
The British did not want to fight the United States, whether localized to the seas or otherwise, and they had, in fact, repealed the Orders by 23 June, 1812, five days after the United States declared war. Of course, there was no way Madison could have known, and when he did find out about the repeal, he opted to wait to hear how Great Britain had responded to his declaration of war before ceasing hostilities.
The third cause was by a wide margin the most pernicious, and even if the British had totally relented on the impressment question, hostilities were very likely to continue. At issue was the simple fact that the newly created Native Confederacy in the old northwest wasn't a British political gambit at all, it was an expression of Native sentiment to unite in their opposition to the United States. The British may not have gotten involved, and had in fact suddenly forgotten their promises to their Indian allies when the US looked as if they might provoke a shooting war - most recently in 1794, following the Battle of Fallen Timbers. But in the United States, the belief that the British were behind the movements of Native groups and aggression totally overlooked the independence of these efforts, and had already fought at least one high-profile battle against the new confederacy before declaring war against Britain, at Tippecanoe in November, 1811. It was very much still an issue, and the two figureheads of the movement, Tenskwatawa and his brother Tecumseh, were still building a confederacy and were still looking to assert Native sovereignty.
And of course, once either side started shooting or taking territory, the war sustains itself on simple inertia. The US lost Mackinac Island in July, invaded across the Detroit river in the same month, then lost Detroit in August, and launched a failed invasion into the Niagara by October. A series of naval actions brought some early success to the US navy, and regardless of whether the war had started pointlessly or not, Britain couldn't just sit by and let the US chip away at their territories and trade.
So, a long way to say that while there was definitely the sentiment on both sides that the war was pointless politicking, the war itself was considered justified by the US government with enough popular support to mobilize the military. It would not be outside the realm of possibility for a British officer to express the opinions in Cornwell's book, though, but not being sure of the exact content of that book I can't speak more specifically.
The two major modern works on the war are Latimer, 1812: The War with America and Hockey, 1812: A Forgotten Conflict. You can also read Madison's war address to congress online here
The War of 1812 is rife with contradictions and on-going debates about the causes for war, the motives of the participants and even who "won". No land was exchanged (Britain wanted to keep its conquests in Maine), as borders returned to the state they were before the conflict. It was a draw. The peace treaty declared it as status quo ante bellum.
Most historians agree that the issue of British impressment of American sailors and the related issue of neutrality rights of its vessels were US grounds for war against Britain. But while impressment was a serious issue -- up to 15,000 US sailors were impressed into the British Navy during the Napoleonic Wars -- the British also had legitimate cause to search US vessels. American statesmen would admit (privately) that about half of all sailors on US merchant ships were in fact British subjects.
Lord Liverpool, the UK PM, wanted a more accommodating relationship with America and had already rescinded the Orders-in-Council that permitted the search, seizure and impressment of sailors on US ships, but the US was unaware of this when Congress declared war in June 1812. Had this news arrived sooner, who knows how Congress may have voted.
US expansion westward had long been a national ambition. In the lead up to war, the chief agitators were the frontier statesmen, or "war hawks". They saw the war as a chance to finally extinguish British influence in the northwest and sever their alliance with the native peoples, who sought a native homeland in territory Americans wanted to settle. So while the invasion of Canada was not technically the only goal of the war, there is little doubt that attacking British territory was also a convenient opportunity that they exploited. New England was mostly opposed for practical reasons. They enjoyed trade with the Maritime colonies and feared the strength of British naval forces, with the port of Halifax nearby.
So, in essence, America wanted the respect as a nation that it believed it had earned in Yorktown ... but the greed for more land westward was also an opportunity that war offered to them.
Britain was in a total war with France -- military, political, economic -- and they were irritated that neutral American merchant ships were bypassing their blockade of France and trading with the enemy, and sapping the manpower of the British navy by employing so many of its deserters. They were outraged that America would attack them, while the British were fighting for their survival against Napoleon.
The "winners" are debatable, depending on which side of the Atlantic, or the 49th parallel, you sit. America got its respect within the community of nations, while Britain defended its Canadian possessions from invasion and conquest. But neutrality rights and impressment, the main causes for war, were not even mentioned in the treaty.
The clear losers were the natives, who were ignored at Ghent in 1814. There would be no native homeland and American expansionism would continue westward to their detriment.