No, you can hold in a collet and run with a live center. As long as the action will fit up inside your headstock... or your barrel is long enough to pass through the headstock. See some pictures I posted in the suppressed Contender thread.
Done it a ton of times. Most of the time I will cut the thread on a lathe and then use a die to hand-chase the thread to remove burrs. But not to cut the actual thread. That can be really challenging. Can it be done? Absolutely. But it is much easier to do on a lathe and use a die for touch-up.
For some Troon moron to do it in a dorm room or his parents basement.... and then fit an actual suppressor. Which probably he cannot get... short of 'adapting' a solvent trap (which has to be drilled straight). and it gets tougher.
Dooable? Absolutely 100 percent. But it does take some skill. Ask
@Threadcutter308 or John Baker or Frank Green or anyone else here who works with barrels and steel. Heck, it can be fitted with a needle file and a whole lot of patience and some lapping compound. I can cut a thread with a triangular file if you give me long enough. Easy? Nope. Dooable? Yup.
Sirhr