this my be strange question but is there a min prop length

No, not really.

If you go short enough maybe something like a rotoflex coupling may be more appropriate.

No there is not. I have even seen drag racers with no prop. The gearbox output is directly connected to the diff with a UJ!

There probably is for a live axle..

Length isn't relevan't, but there is a maximum angle for UJs, so you need to make sure that the prop is long enough to keep the UJs within their working limits for all possible engine/suspension movement.

Using only a single UJ between gearbox and diff would require near perfect alignment, otherwise you would get cyclical speed variation which is normally cancelled out by having two opposing UJs.

interesting read below.
http://www.iedls.com/asp/admin/getFile.asp?RID=10&TID=28&FN=PDF
from here.
http://www.iedls.com/Education-Zone.asp