Depends on what "Annex" Means
I think Denver would be the logical capital for a United States faced with the situation you describe. However I think if anything that grants impetus for it to NOT be the national capital for the USNA.
Historically both Washington D.C. (US Capital) and Canberra (Capital of Australia) were created out of whole cloth in part to unify the burgeoning nation they would be the capital of. Both were situated more-or-less in the geographical center of their nation at the time. Canberra was actually created on the exact midpoint between two competing claims (Melbourne and Sidney). Even given the destruction of the previous capitals and utter lawlessness in Canada, I can't imagine the Canadians would be thrilled by a Union. Likewise I can't imagine the US Army is actively conquering Canada when Kaiju are wrecking whole swaths of the US. So I'm imagining more of a "mostly peaceful" marriage-by-necessity USNA rather than some sort of US military campaign or active begging on the part of the Canadians.
If the above is true, there would be a LOT of pressure on the Canadians to be distinctive members of the USNA. I would imagine that if Denver became the New US Capital (and there are many reasons why it should be in your timeline) The USNA National Capital would NOT be Denver. It's far away from Canada, it's already the US Capital/a US State Capital, and Canadians are already going to be a minority. 454
Allow the nation to be ruled from the US Capital and Canada isn't a thing anymore in any respect. It just becomes a scarecly-populated backwater of the US, regardless of the name change. Likewise American pride/politics would likely shy away at ANY Canadian city being the USNA Capital.
A compromise bet would be to found a city on the border that straddles the two nations (much like Canberra and to a lesser extend D.C.) to show "unity" and is something that doesn't have the baggage of already being a state/national capital. However, in the middle of fighting a massive Kaiju invasion with presumably millions dead that seems too difficult/wasteful even for politicians. So instead I would imagine some large town or minor city close to the border on the US side would be used as the official USNA capital. There are a ton of contenders like Sault Ste. Marie (A US AND Canadian town right across from each other in Michigan/Ontario), but without a map of your <PERSON>-devastated regions I can't comment on what town would be best. There are better choices but those are all on the east/west coast and I assume are destroyed in your timeline.
TL/DR: Your choice of Denver makes perfect military and political sense for the US. But for the USNA Canada would likely have serious political problems with it. A city on/near the old border would be the likely compromise position. 454