Does it conform to the etiquette of this (rather hot-headed) site to invite an opponent via message to an after game analysis?

Sure if you do not over do it and do not be offended if he/she refuses.

Yes. It's OK for you to ask, and it's OK for him to decline

You should probably already be talking to them, springing the question out of the blue might seem weird.

I've done this, but only with friends here.

I guess I should be very careful.