Yes. They do.
For the past 15 or so years the Sr. Little League World Series was held less than an hour's drive from my home. To qualify to play in the Senior League a player has to be no more than 16 years old by a certain date, although the timing of the SLWS makes it possible for 17 year olds to play depending on their birthday. I can't count on both hands the number of young players I've seen come through the Sr League WS who went on to play MLB - inclucing Xander Bogaerts who was signed by the Sox within a couple of weeks after my having seen him play as a young 17 year old.
It's a true World Series with four teams from the US as well as teams from Canada, Europe, Asia, The Phillipines, etc., all of whom have won numerous tournaments to qualify for the WS.
But my point here is that these teams bring maybe a couple of hundred fans with them and believe me when I say that they CARE about baseball. While the number of fans isn't big at the same time many of them come from half way around the world (at their own expense) and many of them send broadcasters who do play-by-play over the internet in their own language.
So yes... they care about baseball and national pride.