It could not trap or launch CTOL aircraft but, depending on the heat resistance of the flight deck, it might be able to support the landing and takeoff of V/STOL aircraft like the Harrier or F-35B. And it might be able to refuel them if it has the correct fuel types aboard and can connect to the aircraft.
But you would not be able to base these aircraft aboard the ship because it would lack the maintenance facilities to keep them flying and the ship probably does not have the ordnance storage needed to keep them supplied with bombs and rockets for very long.
They have some V-22s on order so there is a good chance the deck is heat proof. Ospreys are even worse than fix wings jets for deck heat because the exhaust from their turbo props just blasts straight down at close range the whole time their engines are on.
Assuming its elevators can take an F-35, a ski-jump would be a pretty neat addition for optimum performance.