I am not clear what you mean by "between the modulation".

The full feedback process for improving modulation characteristics attempts to make the transmitted signal as close to a perfect rendition of the ideal waveform as possible, This will probably reduce noise as well as signal distortion. It may even show a close to the carrier phase noise improvement depending on the design. When the SSB modulation goes silent the transmitter should go silent within the capabilities of the feedback loop. Outside the loop bandwidth there MIGHT be a small increase in the transmitter's noise floor.

With fixed predistortion (such as learning the precise D/A transfer function) the signal generation process is improved which will reduce IMD products and such. It may even allow for digitally compensating for the transmitter's linearity. This MAY need frequent calibration as it may be sensitive to supply voltages and the like. Temperature changes will almost assuredly alter the curves. But it will not make any material changes to the local oscillator noise characteristics.

I've noticed in the past that the average ham transceiver has nothing near the signal level to noise floor level characteristics of the receivers. That is largely a separate issue that will take some serious design efforts to change it. The goal of the whole exercise should be to make at least the next adjacent channel usable from a co-sited antenna with the transmitter running full power and as small a spacing between the two antennas as possible. There is a lot of room for effort here. And at present to my somewhat dated knowledge the transmitter is the most fertile ground for this effort at this time.

{^_^}