It can't carry aircraft/spacecraft for interplanetary travel.
Anyway, with a big enough rocket we would theoretically get something as big as a modified destroyer/frigate or aircraft carrier into space, right?
The thing is, an aircraft carrier is a very useful vessel, but it's designed to work in a very specific place: on Earth in a proportionately sized-bathtub. As noted, artificial gravity of some form is mandatory, and the only ways to do that right now are tricks involving spin or acceleration. So let's design this thing with two counter-rotating habitation sections for artificial gravity, and a fixed central axis section with the engines, any dangerously radioactive devices, sensors, and auxiliary vehicle bays (since landing on a spinning habitation module is unnecessarily tricky).
As far as those auxiliary craft are concerned, what are their missions? Space combat? Planetary landing? Each will have vastly different technical requirements, and a craft that can land on an Earth like world and take off again is beyond our present technology. So we have to assume either a much more energetic fuel supply than anything currently used (antimatter?), an engine that is ridiculously efficient, or possibly a means of nullifying gravity to lessen the apparent mass of the craft and its cargo (and that last bit nudges us dangerously close to science
fantasy.
As you can see, a vehicle properly designed for its environment comes out looking very different from one designed for a different environment, even if the functional requirements are the same.
As far as getting a destroyer or frigate or even a carrier into orbit ... yes, in theory, but the rocket involved would be enormous, and there wouldn't be just one of them. Maybe a cluster of Orion-style nuclear pulse detonation engines would do the trick, but I'd like to observe that launch from a ... safe distance.