Earlier quoted context omitted.
Yes, it is much more precise to state that they must be replicating in order to mutate. I've edited my comment to reflect this, Thanks :) If RNA is damaged and changed and the virus particle is destroyed or for some reason never replicates, I don't count that as mutating, but then again what do I know.
bacteria mostly need to be replicating to spread mutations as well. There are mechanisms for bacteria to uptake dna in the environment and incorporate it (e.g. antibiotic resistance). But without replication of the bacteria the resistance wont spread. One interesting point is that in general biology they teach that lamarckian evolution doesnt exist, but bacterial uptake of DNA demonstrates that it does exist.
The Sars-CoV-2 virus (provisionally) doesn't seem to infect and then suppress only to re-emerge later in a new infection, or hang around as an active infection for months. People get sick and their illness lasts a big armful of days.