It does.
Class defines it's Write Speed Mainly.
I have 2 fully working, not fake 8GB Class 4 and Class 6 Cards.
Class 4 Reads at 11Mb/S and Writes at about 4-5MB/s
Class 6 Reads at 16MB/s and Writes at about 7-8MB/s
(Just my Pc Reads on tests and such, is effected by my slow PC... I think :/)
Class 4 Read Speed is good enough for all game so far, the writing is a bit slow when saving big game like DQ9, HG/SS etc... and I have noticed the Class 6 makes it faster at this.
So if you've got a few £/$'s extra, grab a Class 6 Card and if not, don't worry, Class 4 works fine.