About rocket propusion

In its basic form: No. The rocket is treated as pointlike.

In a more realistic approach: Yes. During its initial rise, the center of mass drifts downward but is still aligned with the thrust vector, so the rocket is still essentially point-like.

But once the rocket leans sideways to enter orbit, the c.o.m. moves off-axis. An axial thrust vector would now impart torque. This has to be compensated either by aligning the main thrust vector or compensating this thrust through aerodynamic pressure or reaction control thrusters.

Going even more detailled: The c.o.m. is never exactly on-axis to begin with. Fuel splashes around and other rocket systems are not exactly balanced either.