First Person Spaceship SIM possible?
It sounds like it could work with the right players. On RPOL, GMs can edit players' posts, but players can't edit other players' posts. It would work better if each person were in charge of a different part of the ship, like Engineering, the Bridge, and Sickbay. It would get more difficult if you had multiple players filing logs in the same part of the ship unless people took turns and respected others' posts. I think with a few ground rules it would work really well as a pbp, but a Google Hangouts or a wiki-style roleplay might be easier to manage if players need to edit others' posts.
Also, as a player, I would be a little leery of other players editing my posts, but I've never done a SIM before as you describe, and with some experience and a good understanding of what's appropriate and what's not, it sounds like it could be a lot of fun.