Yes. 1.5 is 'slow' by today's standards, but it is much better than dial-up and plenty fast for xbox live.
You're main concern is with lag and that actually has nothing to do with your max bandwidth. You're worried about latency, which is something entirely different. It would be possible to have a 100meg connection and have horrible lag, while a guy on 1.5 has none.
DSL, on the whole, will get you lower latency over alternative connections like cable or satellite. Until I moved a few weeks ago, I was using 1.5m service and had low latency for gaming.