Although there is some evidence – limited studies blah blah – that some bacteria under stress experience higher mutation rates and hence evolve more rapidly. (There is also some evidence for limited inheritance of acquired characteristics in epigenetics, although the term “acquired” might be pushing the envelope – TL;DR is that if one of your ancestors undergoes an event that results in turning some gene on or off, you may inherit the new state of that gene. The variation was already implicitly present, but its expression was the result of a life event, and it is potentially heritable.)
I have no idea whether there’s anything in the cellular environment that might cause Covid-19 genes to do a better or worse job of proofreading the next generation.