There's no multiplayer anymore for SR2, period. PS3, 360, Steam or GOG. The online aspects ran on Gamespy, which went down forever over a year ago - and don't expect GOG to emulate an entire online infrastructure for the largely forgotten multiplayer component for a mildly popular 7 year old game. The best I can offer is that you use Hamachi to trick the Saints Row 2 LAN co-op into doing direct IP connect play with a buddy.
EDIT: weird, quoted the wrong thread O.o.
It would be nice if they implemented it, but i'll still take DRM free over steam any day.