Will the US annex Canada?

The answer: kind of. An absolute takeover is unlikely, but subjugation is highly probable.

Canada has a lot of things going for it that make it hard to fully annex:

1) It's geographically huge. It's hard to physically control that much territory.

2) The citizens are more healthy, happy, and cared for, which means they're in a stronger place to resist, and they have more to lose, so they'll fight twice as hard.

3) The US doesn't have a big enough military to enforce martial law in Canada, while also going after other juicy targets.

It's too close to the US to not be tempting in terms of national resources, but it's not a satisfying enemy for an authoritarian regime. It's too benign as a target for hatred, and not something they can use to rile up their base. So, it's likely that Canada will not be under total control, but rather, subjugated.

This means that the government will cut a deal with Canada that makes it look like it's under US control - but for the most part, all the US will likely be doing is something like taking x% of the country's tax revenue, and enforcing some social norms (part of being part of the "empire" as a territory).

Canada may not want to agree, but this may happen anyway, because the US has the power to say things like, "[you'll lose all our trade/we'll sanction you/we'll tax your goods] if you don't [give us your mineral rights / hand over your dissidents / accept our social rules]".

It's hard to stand up to the most powerful military in the world, who is also your top trading partner, and only contiguous neighbor.