Don't think that would be all that smart to that unless you like GLITCH pokemon and corrupted save files.
Just tried linking up Japanese Silver and German Crystal. Initializing trading caused Crystal to freeze on the "Please wait" screen before the Pokemon selection, while Silver shows junk for the trade partner's name, because of the different character sets, and party of Pokemon... or wait, correction. Pressing cancel on Silver caused Crystal to "unfreeze", which also shows junk for the other player's name and Pokemon. In fact, I can even scroll past the 6th Pokemon on Silver's side here... So yeah, trading won't work, and if that's any indication, battles obviously won't either.
