Could a tilt quadcopter use turbofan engines?
In a way, this has been done already half a century ago.

When NATO decided to try a VTOL strategy, the Harrier was not the only result. There was even a supersonic VTOL fighter, and it used swivelling engine pods at its wingtips, much like the V-22 does today. It was the VJ-101C, developed in Germany and first flown in 1963.


VJ-101C in flight. Note the opened intake door aft of the cockpit where two additional lift engines were complementing the thrust from the wingtip engines (picture source)

While the VJ-101C used six Rolls-Royce RB145 turbojets, a later production version was planned to use turbofan engines. NATO changed it's mind before the turbofan-powered version was built, however.