Turbines don't work in the space, there is no air.
It might be usable as the first stage of an orbital, or suborbital vehicle.
The main problem with it is not the energy source, but that the size of the drives are too big.
The maximal lift mass of the largest plane ever built, the Antonov An-225, is 640tons. A Soyuz total mass is around 300 tons, more than half of it is its first stage.
However, the maximal speed of the Antonov is around 800 km/h, which is nowhere from the some km/s speed of a Soyuz after its burned out first stage.
To have a supersonic first stage is not impossible, mainly engineering reasons are avoiding it (it could work, but with rockets can go better). And note, we have very few technology to build large supersonic crafts. The largest is the Tupolev Tu160, a Russian strategic bomber, its maximal takeoff weight is 275 tons.