The first thing to know about a Turret Lathe is that it is not an Engine Lathe.
Looking at the link, I'm not really sure that this particular machine has threading capabilities. The ad says Hardenned and Ground Lead Screw which leads me to believe it does. We have two Turret Lathes, and neither do.
http://benchrest.com/attachment.php?attachmentid=18902&stc=1&d=1485609456
Turret Lathes are historically production machines, designed to run multitudes of parts, within the capability of the machine, at a rapid pace.
If you already had this small Turret Lathe, (and it had threading capabilities), I suppose you could figure out a setup to do barrel work.
But, I certainly would not buy it with that purpose in mind.