It's possible, but there are some other things to check first. The set-screws that are in the pulleys can work out and cause the lathe to make some noises like the bearings are going. Sometimes just tightening those set-screws can sort out a noise problem.
Don't get too crazy tightening them though as you don't wish to strip them. You can tell by a bit of fooling with them if there is any slop in the pulley to motor shaft or pulley to spindle. Basically if you can get the pulley to rotate slightly relative to the shaft, the set screws have loosened up.