Backup copy job does not run Fulls, instead it just pulls all the changes the changes that took place on the source side since last synchronization. During every run backup copy job performs a health check that calculates checksums for data blocks in the backup files stored on the target backup repository and compares them to the checksums that were previously stored to the backup files. So your Backup copy job will work in the same way as before - just pulling new blocks.
Will the next backup copy job also run a full backup of the last restore point which would be an full active?
No, it will be still an incremental. Actually, backup copy job is always forewer-forward incremental and does not produce intermediate fulls (GFS is another story).
Another thing that you should keeo in mind is that your backup copy job does not copy anything until at least one new restore point is available, thus your backup schedule might be broken if your active full takes too long.