No, the ship appears when you log back in. Assuming you were standing on it when you log-off, you would be standing on it when you log on.
There is no problem in this regard, you just log-off whenever you want on your ship, it vanishes shortly after you, and when you log back in its there as if you never left. ..I think? its possible someone could attack your ship in the time between you logging-off and when the ship vanishes, but it's never happened to me.
You could however lose your ship to someone attacking it with cannons, manually attacking it with a pistol a ton (especially the floaty-reactor), or explosives (although they arent crazy strong). You could lose it to wind-walls/storm-walls/sand-walls from damage in the later two cases (as they actually damage parts, so be redundant, or just from being pushed out of the sky. Your ship/player dies if it goes wayyyy too low. Having a heavier ship helps fight the strong winds in the walls as does wings i think. Sails get destroyed near-instantly in the walls, so you need a bunch of engines. And the later walls turn you around and you can't see through them so you need to find compass-tech. Also it helps if your reactor isn't near its limit, as it seems it can go up/down with more speed/force if it's not just barely keeping your ship afloat.