Direct answer: Very often, yes. The receiver is the device that actually listens for the transmitter’s radio code, so replacing a receiver can change which remotes work even though the gate-opener motor and control board stay the same.
A useful example
Eagle’s EG640, EG642, EG643, EG644, EG646, and EG654 Chrome controls are documented around the EG650/EG652 receiver family. If an Eagle opener has a different third-party receiver installed, the correct remote follows that receiver’s system instead.