In my experience, no.
I have had maybe two or three incidences of a rover failing to fix/stay fixed, and turning off GLONASS cleared up the issue. I believe it was a bad or missing ephemeris file. But that is not what you are asking.
I guess tracking fewer constellations at both base and rover means less information being transmitted in the correction message by the UHF radio, which means longer battery life…
“…people will come to love their oppression, to adore the technologies that undo their capacities to think.” -Neil Postman