Not always I'm afraid...
If your performance calculations for your flex take-off have a very low V1, then sometimes, that V1 is lower than Vmcg for Full thrust T/O. This depends on how your performance is calculated, and can be an issue if your airline uses min V1 as standard for flex. take-offs or when RWY WET.
Therefore, you should never use a V1 that is lower than Vmcg full thrust just in case of your said scenario or a panick reaction by PF at V1...
Remember that V1 is calculated for your reduced temperature thrust input, Vr and V2 are calculated for actual aircraft mass.