The log chain doesn't break as the way availability groups work is to ensure the LSN's match between all replicas, so there is never any drift in the chain.
With that being said as long as you have all the logs since the full be that from A or from B then yes you can restore to a log backup.
So if the last full from B was back in January, but on A it was July, then you would take the July backup and replay all logs taken from A and then any from B after it was failed over.
But remember backups are worthless, it's the restores that will save your bacon, so you really should be testing all this out and ensuring you can continually meet RTO/RPO deadlines etc.
I personally HATE CommVault and really any 3rd party backup software (with a few exceptions), I would much rather backup the databases to a UNC path common to all replica's using something like OLA, then CommVault would go and do a file level backup instead of that server and secure the BAK/TRN files and not do it's VSS snaps that it does as that just causes more issues than it solves in our environment.
That way I control the backups, and I control the restores and I know what I can achieve to meet the company RTO/RPO's without relying on other teams getting files out of vaults etc.