At 4" you are good to go, any problems will happen inside the spindle, you may easily run such a small diameter at the maximum speed that the machine permits, I suspect that this is less then 5000 thousand Rpms.
Have at it.
Do not however hang 4' out of the back of a lathe without dedicated support, this will likely end in tears.
Have at it.
Do not however hang 4' out of the back of a lathe without dedicated support, this will likely end in tears.