Of course not. It is a terran fighter pilot now.
EDIT:
...Okay, so it is. </spam>
Seriously though, I don't think prone position would be too stressful. It isn't too bad on a rifle range while shooting, and you could always tilt it upwards some 20-30 degrees depending on pilot preference. The "bat-bike" position showed in the screenshots doesn't look very natural IMHO, regardless of what kind of flight suit the pilot is wearing...
My suggestion would be to either have the pilot leaning more forward so that the legs are actually behind the torso, while being supported on some kind of recliner or whatnot, or have the pilot lean backwards. Or you could steal a page from B5 and use a StarFury setup - just strap the pilot on the back wall of the cockpit in an upright position.