They can always use FSOpen, after cleaning and fixing. Or if they do make a new exe with a new source code, the FS2 SCP still wouldn't die so easily. In fact, FS2 being open source and an Interplay FS3 being not-open source, would mean FS2 SCP still being used widely. Maybe even more widely than a FS3.
Though I'd miss the Volition logo over the intro.
No, they can't use FS2_Open because
a. it's based on Volition's source code and
b. it's open source licenced so it's commercial usage would be a copyright/licence infringement.
Furthermore like was already said, any new engine would most likely be written from scratch... and adding compatibility to FS2 file formats (FS2-style POF's, VP's interface etc. etc.) would not be commercially viable, it'd take way too much time to get everything in the new game engine work with old data as well as all the new stuff. Also I doubt they would invest as much as volition did to moddability - though if they were really smart, they would, because that's essentially what kept FS2 alive in my opinion.
I agree that FS2_Open likely wouldn't die, and even moreso it likely wouldn't even compete with FS3. Why? Because of all the community stuff going on based on FS2_Open, not all is even FreeSpace related (total conversions anyone?) and not all of the campaigns are post-capellan histories contradicting any official FS3 storyline (not that people would care all that much, seeing how popular fanfiction is anyway

).
I see two possibilities; if FS3 were moddable and exandable (if they opened the source to that one too at some point), it would probably take a parallel position with FS2_Open as a bleeding edge engine, but FS2_Open would retain all it's good points - low system requirements for a game that looks so good, for instance. And all the content made for it. And all the coders who know the ins and outs of it's inner workings, and of course the community built around it.
If FS3 weren't easily moddable and not open-sourced, it would probably cause an influx of newbies to FreeSpace scene, take some months of people's time to ogle at new graphics and play the game through a couple times, then people would get back to making new stuff for FS2_Open...