It makes no difference at which order of operation you drill the hole as far as how the hole itself turns out. Indicate to find center and then use a spotting drill to start.
I think it does make a difference in your turning however if you drill the hole first. With the hole already in your work when the tool bit comes in contact with the drilled hole this interruption can cause some problems. Chatter of the bit is one. Another is if you are using carbide tooling it very well may chip the cutting edge of the tool off.