No, it wouldn't. If it peaked at the same time it would be in-phase with the grid - there would be no phase angle difference & no power would transfer. Even if the magnitude of the sinewave were bigger it would still only export reactive power.
The inverter sinewave must be a few degress ahead of the grid sinewave & attempting to "pull it faster" in order to export real power.
Think about generator theory. Remember that when a generator is operating in parallel with the grid controlling excitation influences reactive power & the torque from the prime mover determines the real power - the prime mover is trying to pull the generator rotor out-of-step with the magnetic field created in the stator by the grid. This ripping apart of the two magnetic fields is what causes the generation of real power. A similar process has to happen with the inverter.
Adrian
