Can I still buy AppleCare for my Mac?

mmm...

Did the Apple Store person log-in your system (S/N)? Then they have a record of it in London. So going back to a UK Apple Store (any EU country as well) will have access to the record.

At this point in time you may have a very small window to bring it into a Mexico Apple Store to have it repaired it all has to do with how Apple collects the data and moves it around.

So, let's say you got the Apple Care+ today you would need to wait a bit before getting it serviced in Mexico assuming you could get there :-}

Bottom line I think you're only throwing way money here trying to pull a fast one as I'm sure the records of your visit will beat you, and in doing so will negate the free service you are hoping to get.