Only if said enlistment involved:
- Long, 3- or 6-month deployments away from one's home system, depending on ship class.
- Doing endless patrol loops between an assigned set of stars for that time period.
- New, bushier and more outlandish facial hair styles on the Holo-Me page for the duration of the deployment
- Periodic comms from your chosen power promising a sweet port call 'next week', followed by their cancellation the day prior to the promised stop so the ship can instead be sent to support 'the mission', and which inevitably involves doing endless patrol loops around a different set of stars.
- Game connection to your real-life e-mail and phone, so that at any time, day or night (let's be honest, probably night), you can receive a message that you need to get out of your rack and log in so you can participate in drills.
- Placing NPC sailors on the bridge with you, who you only get along with because there's nobody else to talk to, but with whom you'd really rather not have to die.
- Placing NPC sailors in the galley whom you never see anywhere else on the ship, and are pretty sure only exist to stand in front of you in line at chow time.
- Space legs/ship interiors to allow for weekly field day (cleaning) of the ship, with an NPC Chief or Ensign included to look under/behind all gear to ensure you didn't miss anything.
- Assignment of extra missions after each successfully completed mission that decrease in value and increase in tedium for each additional success.
Wouldn't want to break the immersion, after all.
I suppose I should have elaborated on my earlier endorsement of the idea with an added: "But not if it's realistic. I'd like it as an option if the in-game version was more along the lines of what my recruitment officer told me."