You have some replies already, I'd just like to summarize, perhaps clarify a bit and also expand a bit on what has been posted already:
COPY_ONLY (I'll call it CO from now on) can affect restorability in two scenarios:
One is when you take a full backup. A subsequent doff backup is based on the most recent (non-CO) full backup. So if you want to take a full backup without affect restorability of diff backup, then do the full backup as a CO backup.
The other is a log backup. When you restore log backups you need an unbroken chain of log backups. You can take an out-of-bands log backup which won't be needed for a subsequent restore process by doing that log backup as a CO log backup. Basically, it won't empty the log.
A full backup does not affect restorability of log backup. CO is not needed here.
Another aspect, though, is if you want to rely on SSMS and its backup history to do restore. In some cases, CO backups are not in the proposed restore sequenct. But in other cases, a restore sequence is based on a CO backup and if that backup doesn't exists on disk, then you won't be able to do the restore from SSMS based on the backup history. It is a bit of a mess and I've reported this to MS several time, but I have no hopes for this being fixed.