No, molten salt reactors are not the right technology for nuclear propulsion. The idea of a nuclear thermal rocket engine is to heat up very light molecules to very high temperatures, and so to achieve higher exhaust velocities than chemical rockets. If you plug a higher exhaust velocity in the rocket equation, you end up needing less fuel mass for the same cargo mass. In practice, the best nuclear thermal rockets achieve a lower temperature than chemical rockets, but they can dedicate it to heat only hydrogen (H2), rather than the combustion products in chemical rockets (such as H2O or CO2), so overall the exhaust velocity can be approximately twice as high.

Still, temperature is quite important, you want the core of the reactor to run as hot as possible. You are limited by the fact that you don't want the core to disintegrate. The NERVA project [1] achieved temperatures in excess of 2200 K.

Molten salt reactors are designed to reach about 1000 K. That gives up most of the benefit of using a nuclear reactor. You would still beat chemical rockets, but only by 25%, not by a factor of 2. Why would you do that? If you build on the NERVA project and use TRISO fuel (which was not available at the time) you can end up with a specific impulse of more than 1000 s, which is 2.2 times higher than what the best chemical rockets can deliver, and 2.85 times higher than SpaceX Starship.

[1] https://en.wikipedia.org/wiki/NERVA#Reactor_and_engine_test_...