Good Question. I am undecided. What do y'all think?
I don't think Canada itself will stay that much in the Commonwealth camp, they're too close to the US and ITTL the Free Americas/OAS is a much,
much tighter organization. I'm not saying they'd straight up leave per se, but that they'd look more southward than east in terms of international policy (maybe staying tied to Britain for sentimental reasons, and not much else).
Besides, I got the impression that good feelings between the UK and Canada (and Ireland, by the way) would deteriorate pretty quickly as a result of the Brittany Debacle. I would use the hint dropped in the "Where Are They Now" portion of the original thread, and have the Commonwealth consist largely of Hong Kong, Singapore, Gibraltar, the Falklands, British Honduras, Jamaica, Guiana, and Cyprus; Canada, Australia and New Zealand may not necessarily walk away from the Home Country, but I wouldn't say they'd be as tight as IOTL either (how Britannia conducts herself in the Indian Civil War might play a role here).
EDIT: Argh, reading comprehension are not my friend

In response to the question, I think parts of what was British India might remain part of the Commonwealth, but the bulk IMHO will fight for independence. A couple spots that could remain loyal are Bangladesh, Ceylon/Sri Lanka, and maybe the Tamil region at most.