The nozzles of the front engine can be directed downwards OR backwards. So, the front engine presents no "dead weight" problem.

But there might be a couple of geometric problems that need special consideration:

1) In order to put the 2 front nozzles ahead of the CG of the aircraft, the front fuselage would have to be pretty long since it has to accomodate the length of the front engine, as well as the cockpit, the radar, etc.

2) The engine(s) is the heaviest single item on a fighter aircraft, put tingan engine in front of the front nozzles will moves the CG of the aircraft even further forward.....

It would be interesting to see how long such a VTOL fighter will turn out to be!