I guess that you put these databases on an Availability Group, because they were deemed critical enough to warrant an HA/DR solution. And now you are telling me that log backups are not happening? That could be acceptable with a tier-3 system, but not a system that requires an HA solution. If the backup tool is not working, I would schedule native backups in the meanwhile to minimise the damage in case of a disaster. You do have an SLA with an RPO and RTO don't you?
As for your question, I can't but see that there will be an outage, as it will not be possible to write to the database.