even if it was possible, who in his right mind would want to do that! USDT price is currently -9% under $1 meaning it is worth $0.91.
and this is while you CAN withdraw bitcoin and sell it in another exchange.
It would really depend on what your purpose is. For me I would prefer to use USDT as a speculative medium to use so I can move in and out of an exchange with ease while having the properties of a cryptocurrency like keeping them in a wallet you control. Ultimately if I am not investing or trading I keep them in Bitcoins.
does this mean you can run your own (desktop) wallet of USDT? because i have always thought you can only register on the tether.io website and have an account there which sends and receives USDT and there were no other way of using that currency despite it being the same as bitcoin at code level!
Did I say it is exactly the same as Bitcoin? What I said is it will be more useful than USD because you can withdraw USDT from an exchange to a wallet you control. If you feel safe holding USD in an exchange then it is up to you. Wiring fiat back and forth is not a good choice either.