little late to this, but it's a fairly simple answer: basically, no.

The British strategy along the coasts and up and around the Chesapeake wasn't meant to be - or capable of being - a permanent invasion force. Instead, it was organized around raiding and disrupting the concentration of American forces. This was made possible essentially due to the overwhelming naval power of the British forces; as soon as the British bottled up most of the American east coast ports, the threat of a frigate getting in among raiding groups was less likely, and men like George Cockburn had a fairly free hand in clandestine raiding. They were further helped by actively assisting the enslaved in the area, who sometimes helped them by scouting and spying.

The capture of DC was a coup, but it wasn't expected to end the war. It was an opportunistic attack based on exploiting the strengths of the British forces against the weakness of the Americans. The British could land troops anywhere, nearly at any time, and the expertise in raiding and the local knowledge accrued by the recruitment of the formerly enslaved made them a terribly flexible force. When Sir George Prevost, the governor-general of Canada, wrote to Alexander Cochrane, the commander of the British Atlantic fleet, about the "wanton destruction of property" Cochrane first imagined seizing larger, more strongly-held cities, but Cockburn suggested making a quick raid to DC, owing to the larger moral effect that the seizure of the capitol would have. But this was still never meant to occupy Washington for long; immediately after, they were to recollect on the ships and strike for Baltimore, even if the storm hadn't hit them.

In terms of the motivation of the attack, it's a little more complicated than as retaliation for the invasion of Canada. Seizing Canada was a public, overt, obvious component of the American war strategy, but in the two years since the beginning of the war, fighting along the border regions of Upper Canada became incredibly intense and violent. Whether through accident or deliberate malice, American troops had burned whole villages, turning people out into the winter without homes, and had even burned mills and other private property, actions which violated the understanding of proper warfare by deliberately targeting civilians, even if they never went out of their way to kill them.

So if, along with raiding plantations and freeing their enslaved populations (a direct attack on the entire basis of American power in the south, and an attack on private property), British forces destroyed private property - like when Cockburn deliberately destroyed printing offices of newspapers that had slandered his name, to the point of personally destroying the "C" types so they couldn't use his name! - then, well, the Americans had escalated first.

But the tl;dr here is that occupying the American capitol was not an aim of the campaign, but raiding it and destroying many of its public and private buildings was. The real targets were major coastal cities like Baltimore and Philadelphia, but due to various events they never seized any of them, though they came close.