He already was taking hydroxychloroquine earlier this year. If he still supports using it, which he hasn't made any remarks saying that he is against it, I don't see the possibility of him taking it being completely out the window for him.
1) He said he was taking it, but provided no proof. If we question whether he actually has the disease, we should question if he ever took the drug at all.
2) Back on May 19th, when he said this, the FDA had an open emergency use authorization for the drug for people hospitalized with the disease. In June, the FDA has withdrew the authorization, and the WHO, Novartis, and NIH all stopped their trials.
Giving what would now be considered both off-label and "experimental" treatment to the President of the United States in a health crisis is probably a career ender if something goes wrong.