The answer is no! There is a diode in reverse on most MOS devices a which will allow the current to run backwards into your circuit.
A thyristor will block the reverse current, but cannot be turned off while the current is positive.
Thyristor regulators turn on part of the cycle and turn off when the voltage goes to zero (or reverse).
If the solid state relay is for AC it has two thyristors in parallel, one for each half pulse. If the relay is DC, it probably has a diode across it which would be a short when the inlut(?) goes negative.
I'm trying to make a battery charger without a final diode in series (save power loss), but the semiconductor internal diodes always foil it.
When the charge voltage goes off, the current wants to run back from the battery into the generator (not alternator which has diodes).