Yes as far as I am aware unless the a/c is operated as multi-crew under the AOC ops manual only the commander can log the time.
With regard to multi-crew time. I have been down this road and there is no problem with using those hours to meet the "500 multi-crew hours" requirement. I recently got my self "unfrozen" with hours accumulated on a B-200 and a CJ both of which are SPA operated in a multi-crew role under an AOC. You do still need a MPA type on your licence.
Good Luck