SQL Server 2012 always-on backup, full vs copy-only

Does this mean I will need to do a full backup on primary if a restore of the transaction log is required?

NO -- You can add t-log backups to a restore of a COPY_ONLY backup

only copy-only and transaction log backups are possible on replica

True.

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

You can restore transaction logs on top of a copy-only full backup--this means that you can use a copy-only backup from the secondary replica along with transaction logs, and accomplish point-in-time recovery.

However, if you are only performing copy-only backups on the secondary replica, you won't have a "real" backup to reset the differential bitmap on the primary replica. If differential backups are part of your recovery strategy, then you need to take full backups on primary. If you every want to use a differential backup, you would need to take a full backup on the primary replica to use as the differential base.