Your assumption is that the United States' goal in the War of 1812 was to annex Canada. Most historians believe that the invasion of Canada was a means to get Britain to talk favorable peace terms. Secretary of State James Monroe stated;

"in case of war it might be necessary to invade canada; not as an object of the war, but as a means to bring it to a satisfactory conclusion"

As for whether the US could've successfully managed the war and annexed Canada in a more traditional victory, it's hard to say. Throughout the war the US faced many financial and political obstacles - the war was unpopular with most of the population in New England, the First US Bank had been closed in the years prior by Madison and Jefferson, and the US Army was just in a generally poor state at the time.

However, the reason the US went to war was mostly a result of being treated like a British protectorate - impressment of American merchants into the Royal Navy, seizure of ships trading with France, arming native americans along the United States' western borders, and as a result of the War of 1812, these things stopped - the British maintained that they had the right to impressment, but they never did it again, and Tecumseh's Confederacy was dissolved with Tecumseh's death at the Battle of Thames, so British support for the Native Americans ended.

The way I've always described it is that in the War of 1812, everyone is a winner except for Tecumseh and the Native Americans.