Well the GB Player guts are a standard GBA, just happens to output through the Gamecube more or less. I have the ez-flash iv which is the one in your picture. I've had no issue running it a gba sp, gb micro, and the DS units that can run it so I'd think it would work fine.
As far as loading it up, yes you can but there are limits.
Basically how it works is that if you want to do GB and GBC stuff, you need to use GOOMBA and GOOMBA COLOR respectively. That said, you can not just load a crap ton of games and expect it to work. I can't remember exactly the threshhold on it as far as a maximum goes but somewhere in the neighborhood I think of 16MB or so will work. At some point the ROM gets too big and it will fail to load at all in flash card via the menu, or the rom will be corrupt and only read only so far into it so some games won't work.
What I did for myself after learning that was to create a Goomba.gb with just b&w stuff, then I did a goombaGBC1 and 2 file which I split my GBC games up evenly. So once you use the goomba builder that makes these, you can just use the software that comes with the card to load them onto the SD card, but you have to use their app or it can and usually will mess things up. Once there, just boot the GBA up, click the game in the shell menu the flash card has and the emulator file with the roms in it will fire up in a moment.
I've looked and it's the only good one left made that has the highest of compatibility. There are a few others but they're picky and smaller, and then you have the old products from years ago and good luck finding any of that, plus they're limited down to like 32MB or 64MB of files at most max while the ezflash can handle a couple of GB of files.
