yes it will play your gba games but if you have a ds phatty then you need to get the orginal size ezflash3in1. the small compact version only fits in the ds lite to make it a slim fit and will not fit into the phat ds.

 

You can also buy a replacement case that fits the larger DS.
Many places that sell the EZFlash 3-in-1 also sell the cases.
I suppose you could also use an old DS game possibly, but Im not sure how it'd fit in place or if it will at all.
I'd say your best bet is to pick up the replacements, they're ususally $0.25 and possibly wont bump up your shipping.