By default copied files (the copies that are created by the actions of the profile) will have their archive attribute enabled (ticked) if the file of which a copy was made also had the archive attribute set. If not, the copy that is created will not have it set either. In other words, the bit-state is preserved by default.

SyncBack can be optionally be configured to clear the archive attribute (Copy/Delete -> Advanced -> Reset the archive file attribute on files once they have been copied) - on both sides. There is no functionality to preserve it on one side and clear it on the other.