Yes. I have some experience with this as this is exactly what I did. But LT is a far cry from being a captain of a ship in charge of hundreds of people. LTs are brand new (and often still in the "college kid" mentality) and with no experience aren't given much more respect or responsibility than privates. We often joke that our only job is to try and avoid accidently blowing up the base.
Hell, most people spend the majority of thier careers as a LT doing random office work around base or in job training waiting to be promoted. Usually it takes two years to be promoted to a 1st LT, and another three to be promoted to Captain. But even when you make the rank of Captain you still aren't given that much to be in charge of. It just means that they trust you to be professional, make smart decisions, and do your job without being constantly watched. Expect 10 years before they trust you to be in charge of anything larger than a small office staff.
Im not quite sure how the Star Trek Starfleet ranks work, but if I had to guess id say that the Captain of a starship would probably be the equivilant of a Colonel in our military. Someone who has 15-20 years worth of experience under thier belt and has stood out from thier peers over the course of thier career as a clear leader. There is no way in all hell they would hand over the command of a giant starship to a brand new officer. Not unless they want the worlds largest government subsidized party bus roaming the galaxy.
