Actual dilithium has a 4-dimensional crystalline structure, that is part of why we haven't been able to find any yet. It's not just a crystallized ordinary lithium.
Also, impulse power does not use the dilithium. The dilithium was only involved when operating at warp speed, as it was used to focus the energy released by the antimatter reaction in order to effectively form the warp field. Even at that, it was a feature only found on 23rd and up century ships, early warp drives ran on pure antimatter power without being focused.
However, I am somewhat concerned that they are trying to build an engine out of a technology that doesn't work yet. To date we haven't made a sustainable fusion reaction for net energy yield, the only exothermic fusions so far have been bombs.
But if we can get fusion to work and provide a net energy gain, I could definately see this being a major boost to space exploration even without warp drive being a viable option for the shuttle in my driveway.
Sadly can't bring home the starship, most of the starships in the franchise were incapable of operating within an atmosphere and had to be parked in orbit for transporter or shuttle basing.
