Unfortunately with 56k its gonna depend on what game your playing, for online RPG's I cant see your lag being a problem, but for the likes of SOCOM, RR6, and soul calibur, the will start to make a noticable effect.
I've never been 56k m8 so I dont know the full extend of the lag in regards to Ps2 online, but I doubt it'll be any different than PC. Meaning if you lag the room/server will lag
