Which GX 620?
Mid tower? SFF? Mini tower?
I'm using a mid tower GX620 right now, and I can tell you straight up that there's only enough room for a single slot card. The PCI-E slot is all the way at the leftmost bracket, and the CPU fan is so huge that it blocks dual slot GPU coolers.
Even then you would need a better PSU than the idiotic OEM one that comes with it, as the mid tower actually supports ATX PSUs.
I was originally gonna buy this GPU: http://www.newegg.com/Product/Product.aspx?Item=N82E16814131330&nm_mc=OTC-Froogle&cm_mmc=OTC-Froogle-_-Video+Cards-_-PowerColor-_-14131330
And this PSU: http://www.newegg.com/Product/Product.aspx?Item=N82E16817171028&cm_re=cooler_master_extreme-_-17-171-028-_-Product
... for my 620, but I've decided on just waiting and building an all new computer, which I recommend you to do as well. If you can't, then go with those.
Also, how much RAM is this 620 coming with? Which processor will it come with?
You're gonna be bottlenecked regardless, but not as much with a Pentium D 945/950/960 that it supports, and AT LEAST 2 GB RAM.
That's still not enough if you aren't running XP 32-bit, but you have to make due with what you have, right?