Even after obtaining a provisional license, you need to retain your U.S. license anyway for driving during the 12-month grace period, otherwise you'd be treated like a new driver and come under all the applicable rules for such (L plates, accompanying licensed driver, no motorways, etc.).
I don't think DVLA should ask for your American license even after you pass the test and are issued with a full U.K. license. I believe they are only supposed to do that with an exchangeable license (i.e. where no provisional/test is mandated, such as for EU licenses etc.).