Update: We've now had a chance to try the US Boot Disc on a modded GameCube and a Japanese Game Boy Player, and we're pleased to announce that as expected, it works flawlessly.
Sometimes, the ways of Nintendo confuse us ... like the decision to release the Game Boy Player in the US in only Jet Black. This has caused the Player to be one of the hottest import items in a while, as the Player comes in four colors in Japan.
The only real "flaw" with the imported Player was the need for a region coded boot disc, which means if your GameCube didn't have a region mod (or Freeloader swap disc), you'd be out of luck. Even so, switching regions or swapping discs is a hassle, however slight.
Never you fear, because Nintendo has started offering the Game Boy Player Boot Disc as a replacement item in their online store. Simply choose "Parts, Accessories, and Manuals", then "Nintendo GameCube", then finally "Parts and Accessories" to find the replacement boot disc available for $15.00. With $5.00 shipping, your total will come to $20.00.
Thanks to Anubis081883 for the tip!