Are fixed wing aircraft with gimbal thrust feasible?
Could you create an aircraft using an jet engine/propeller/ducted fan on a gimbal?  Sure you 'could'; it is feasible by the laws of physics.  But just because you can does not mean that you should.

Setting up multiple points of lift on a manned aircraft seems like a good idea with a lot of advantages but is a Pandora's Box of problems, the not the least of which is the grave risks of single point failure.  Lift and control is totally reliant on balanced lift between multiple engines.  Lose one engine and the craft departs from controlled flight and crashes.  You better hope you have an ejection seat and/or parachute on board.

Some solutions to these problems come in the form tiltrotor designs like the Agusta Westland 609 and the V-22.  But these aircraft have multiple redundancies in their design including a common transmission system between the rotors; in case of a single engine failure, the good engine has enough power to drive both rotors.  Tiltrotors can also glide like regular airplanes and utilize control surfaces during this and cruise flight.

As a final note:  Be careful in putting too much faith in Musk and other Silicon Valley whiz kids speculating about other design endeavors.  The skills required to run a successful software company are often very different from that required to develop other artifacts like aircraft and automobiles, etc.  Musk was a genius with PayPal but nearly went bankrupt starting an electric car company and his development work with SpaceX has been punctuated with a series of spectacular failures.  He also quietly withdrew from his proposed 'Hyperloop' project, I suspect, because he really didn't understand what he was getting into there.