Years ago, we had a few come out with us for small trips, but not traditional deployments. More like work-ups when you are out Monday back Friday. Hate to say it but there wasn't much for them to do. They weren't built into the Watch bill, and since we were working up, we didn't really have a lot of time to train them on anything, as we were trying to get stuff fixed and qualified. They ended up standing a lot of Junior Officer of the Deck.
As a reservist, the official answer is "sometimes". It depends on whether or not there are any openings on a ship that needs an extra SWO. For their drill weekends, it depends on what their unit supports. They could support a fleet or a special group like Military Sealift Command. I've even seen SWOs run SeaBee units.
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