According to this YouTube video which starts with a 5 minutes summary the Liquid Fluoride Thorium Reactor is an extremely safe alternative to the current ones.
Not only Thorium is abundant on Earth, but this technology cannot be used to build weapons, and they automatically shut down in an emergency.
Would this be useful to power rocket engines or at least to generate power to them?
Any form of power generation could be used in space. It's a question of whether it's financially and practically feasible. From a spacecraft perspective mass is a huge contributor to cost - typical estimates are $10,000/kg.
Now from what I've read on Wikipedia about LFTR, they can produce a whole lot of power in this table it seems the most efficient system produces 1000-MW(e) from 700kg of fuel. That lasts approximately 12.5 years according to the reference. Lets assume that that time span is acceptable for our mission. However we probably don't need 1000MW - or anything close to that; depending on the payload you're designing for you power requirements might be tiny or huge but 1GW is larger than I recollect hearing (maybe look into Lunokhod since the rovers are RTG powered).
The question then becomes scale. Can you effectively scale down your 1GW design to 1MW? That might be more in the range that would be useful for spacecraft. You probably can't assume it's simply 1/1000th of the mass since smaller engines typically have larger dry:wet mass ratios. We haven't actually covered dry system mass yet either. I can't find any estimates for the dry system mass (dry mass is total mass less fissile material mass) but typically with anything nuclear related it can be many thousands of time the fissile mass. So a 700kg fissile mass may require a system mass of hundreds of tonnes, or more.
However that all being said, if there is the need for a huge, high power spacecraft like those seen in sci-fi films it may be a reasonable alternative to solar power especially for interstellar travel - at pluto you're spacecraft would require truly gigantic solar arrays to match power with this system.
I would direct you to a documentary by a proponent of LFTR power, Kirk Sorensen, a nuclear physicist with an engineering degree. He spends the first part explaining all the ways in which space exploration has been limited by the lack of a safe and efficient power source like LFTR. He is speaking of enough energy to power a drill to penetrate the thick ice layer on the moon Europa, or heat and greatly extend the life span of probes we might land on cold destinations like Mars, Titan, comets and asteroids which otherwise 'freeze to death', or the ability to power human habitats on Mars or the Moon. As for usefulness for propulsion, it seems the LFTR process actually creates byproducts which can be used as fuel! The whole presentation is very convincing because he has a good way of explaining science; e.g. in one of the first scenes he shows a salt shaker and explains that salt in that solid state, at room temperature, is actually frozen. It would be interesting to hear if his approach has application to the recent (2016) idea of sending a featherweight mini camera at one-tenth light speed to one of the nearest star/planet systems.
We also should consider how practically we can build nuclear powered rockets or space probes which can propel safely. The practical difficulties like radiation from the reactor, the controlled nuclear reaction (either fission or fusion), the metallurgy part which withstand very high temperatures are to be solved. The heat generated by the core engine (nuclear engine) should not spoil the payload. Above all, the engine structure must withstand thermal and mechanical shock produced by the nuclear reactor. The liquid fluorine must be highly efficient to absorb the heat generated to maintain the reaction to proceed further. All these factors plays a important role in developing the nuclear powered rocket.
