Not quite, Dave. In fact, it's like Nevada, but with different designations. You cannot register a vehicle with a Salvage title, but yes, you can repair it and obtain a normal title again. There is no question about that, because that is the only way to register a vehicle. HOWEVER, it will NOT be an entirely clean title. Nevada has a section on the title labeled "BRANDS" where it will say "REBUILT". New Jersey has a section labeled "STATUS" where it simply says "R" or something to that effect.
That variance in branding is what facilitates the process of title washing, as well as uninformed buyers.
Again, given the variances in branding, I've no idea what "Dismantled" means for whatever state labeled it as such. But depending upon the state, you will have some potential options. The best bet would be to see if perhaps you can go for a "Reconstructed" type of vehicle, which given the age/status, who knows if you might not be able to get an exemption. That allows you to rebuild the car as a DeLorean DMC-12. A "Specially Constructed" title is that kit car thing. However, it must be a unique vehicle in the end that was never constructed by a known, recognized manufacturer. Now I've no idea what aesthetics may be on the outside, particularly with brightwork and badges, but with this title you would receive an assigned VIN from the state, and would never be able to legally call it a DeLorean again.
Check with your local state regulations, of course, to see what your options are. But be aware that you're never going to get away from that stigma of a salvage title. Even if your state issued you a clean one, that VIN will still show a it's current status when a historical lookup for the chain of custody is done. If you ever sell it and misrepresent the car in anyway as never having that title (and for whatever reason it was assigned), that would get you into legal trouble by misrepresenting the car since you obviously know about this problem with the title.