It is possible to have moving ships with players inside, however the speed these ships move would have to be, in general, very slow. There is a line of code in 2142 that disables collision calculations with the outside world and keeps things relative to the interior of the ship, provided the ship does not move along so fast that the player gets dragged out of it. This is how 2142 is able to have the titans move while players walk around inside. This is, unfortunately, a rather complex process (however, it is certainly not limited to one per team as some have said here). It is far more likely for you to see interiors of large cap ships such as ISDs and Mon Cals with them remaining static as the sheer size of the vessel requires it to remain stationary and generally requires it to be assembled from multiple static objects as you currently see on Escape from Hoth. On a smaller scale ship, such as a frigate or something it might be possible for you to walk around inside with it moving, with however a significant sacrifice in speed.
Basically, it's very likely you'll see the interior of Capitalships and other vessels, whether or not they are all mobile is not entirely impossible, but not necessarily likely either.