I know that some of the 2004 season EA Sports games have a special feature called EA Sports BIO, which allows you to keep track of stats between games and, with the case of NCAA Football 2004, import a custom player or NFL draft class into Madden 2004. PS2 and XBOX owners also have the ability to import a NBA draft class from NCAA March Madness 2004 into NBA Live 2004. I don't think MVP Baseball 2004 uses EA Sports BIO, and neither does NASCAR Thunder 2004.
LEGO Star Wars II: The Original Trilogy actually uses something like this to its advantage: if you have a save file for LEGO Star Wars: The Video Game on your PS2/GameCube memory card or XBOX/computer hard drive, you can unlock and buy a cheat allowing you to play as characters from the first game in the Original Trilogy (minus any character already in the Original Trilogy game, i.e. Leia or Antilles). While this is redundant since The Complete Saga is a thing, before complete saga came out this was the only way you could play as the prequel characters in Episodes IV, V, and VI.