OK, so I swapped out the .img files on the SD card (making darned sure to protect the existing, US-wide file against accidental overwrite) and checked it out. And in fact, with the Mexico .img file on there, the GPS does recognize locations and offer POI's from that country.
When I tried some auto-routing (e.g., from Zacatecas to a particular point in Puerto Vallarta), the results were a little weird: some segments were turn-by-turn, whereas others were literally just straight lines from point-to-point, drawn with no regard for the actual roads. I don't think I'll worry about that too much just yet, since it seems that the map itself was present, so at least I'll "know where I am". The thing that's a bit clunky is that if the .img files have to have the same name, then I'll need to carry two SD cards and swap them out once I approach the border, 'cuz my unit (Garmin C320) doesn't appear to offer a utility through which to select a particular map.
Although now that I think about THAT, I could easily test it by renaming one of the files, and seeing if I can find a screen where I can choose between them...
Thanks again for weighing in!
The Chief (tm)
Will Work for Fuel
1 Continent / 3 Countries / 4 Provinces / 11 Estados / 39 States