My nephew has a gamecube player for his gameboy games.
He found it at a local game trading story for about $15 and he enjoys it.
The games look just fine as far as I can tell. For the most part they seem to run full screen, but I've seen him play games that had the border. I don't know if it defaults to that on some games or if it's a preference he's chosen. Although come to think of it, I think the border screens are for the older GB games and not the GBA games.
It has all the functionality of a gameboy except the link capability. I mean, for instance in Wind Waker you can use a gameboy to be in constant communication with Tinkle. You can't do that with the player, but if you're looking to just play GBA games then I think the player is certainly a good idea.
I'll ask him when I see him next, see what he thinks and edit my post accordingly.