only copy-only and transaction log backups are possible on replica
Does this mean I will need to do a full backup on primary if a restore of the transaction log is required?
Short answer YES.
From BOL :
A consistent log chain is ensured across log backups taken on any of the replicas (primary or secondary), irrespective of their availability mode (synchronous-commit or asynchronous-commit).
So to answer your question, a COPY_ONLY backup cannot be a part of a restore that involves T-log backups (doing a point-in-time restore). Its whole point is to have a backup set outside regular backup chain NOT impacting the restore sequence.
A full backup must be performed on primary database (cant be a copy_only backup).
Only T-log backup (as mentioned above) can be done on either primary or secondary with a CAVEAT that it wont mess up the LSNs on the PRIMARY i.e it will keep the LSNs consistent - regardless of where you take log backups in the availablity group.
Best is to check the
sys.fn_hadr_backup_is_preferred_replica so the log backups will use the Availablity group backup preferences for Log backups.
Refer to : Performing Transaction Log Backups using AlwaysOn Availability Group Read-Only Secondary Replicas - Part 1