The consequence of too small of a diameter would be whip at high RPM. Without looking at numbers, I think you will be fine with a 40" long 5/8" screw within reasonable RPM but it would be best to do a little research just to be sure.
There is info on the net about RPM, diameter and whip. I will dig around and report back in a bit.
What is the pitch of the ballscrew you are considering? Any idea on max RPM or desired traverse speed?