When you go to jail and they book you into jail they strip you of everything you own and give you inmate clothes to wear as well as inmate shoes.
The inmate shoes and clothes have been worn by many other inmates including the underwear or panties and from what I've heard the clothes are very uncomfortable.
The jail will then put your clothes into a bag and place them in a room where you can get them back upon your release from the jail.
The jail will keep your wallet, watches and any Jewelry you have on you.
So no you won't be able to wear a watch in jail and you wouldn't want too anyway because looking at your watch would make the time seem to drag on slower and slower.
So it's best to not look at the watch while in jail as it will make your time harder.