Yes, the welder is supposed to follow the WPS as written. If you want to include more than one electrode classification, you will need to revise the WPS. However, a entry such as "All E60XX or E70XX electrodes" would be ill advised because it would allow your welder to use any permitted classification, such as E6010, E6012, E6013, etc. Such wide latitude would not be to your advantage if he should be limited to welding with low hydrogen electrode. The WPS should provide sufficient direction to the welder that he doesn't have to guess which electrode is appropriate for the work.
Best regards - Al