At one point, I did play a couple of SFC II games on a 56K modem connection.
And my system was "weak", Celeron 400 MHZ w/64 MB RAM on Win ME, using a 32mb Diamond video card.
However, for the few games I've played on that connection, I had no issues with lag on that 56k, and I actually hosted a 3 player battle or 2, again, no lag.
However, I also had a preety good dial-up connection (regularly connected at 52,000 - 53,000 kbps) on clean phone lines (only dropped when a call came in over call waiting)...
I've also played with that same system on a cable modem, and it was no different. I have also upgraded to a "newer" computer (Celeron 900 w/ 128 MB ram, still Win ME, this one using an Intel integrated video card), and had no issues there, too. On the most recent "big" server, AotK, I had myself, Blade, and a Klingon RM (I can't remember who) on for an ambush mission (the Klingon was the recipient of an ISC ambush), which I initiated, and went off lag free (even though Blade had a carrier...)