No, it provides power to power flight control systems, linked hydraulics and e.g. some flight instruments. You can't generate the power needed to re-start an engine from a RAT.
You can restart by sacrificing height for speed and "propelling" the engines up to speed.
At some point, this isn't sufficient, and pilots need to start the auxiliary power unit (APU) and go through the full restart procedure as though on the ground.
But this is a moot point, given there was no fuel left...
Makes one wonder. Fuel is measurable, not only via fuel sensors, but as inertia expected vs inertia actual by laser gyro (https://en.wikipedia.org/wiki/Ring_laser_gyroscope).
There must have been some pretty deviant values on that screen. Unless the system just "calibrated" those deviances away..