Being that SI Deluxe uses a B&W monitor, and isn't JAMMA, it would seem like the modifications necessary to MAME it would be fairly extensive... Color monitor, new wiring, new CP - basically gutting the cabinet (or redoing everything in parallel with what's there). Unless, of course, you build a custom "J-Pac style" adapter to plug into the existing harness and just set it up to play the few B&W games in MAME - which I can't really imagine being worth the effort... The changes could be done in such a way as to be reversible, but not easily reversible.
That said, it's your cabinet - do with it what you want. Personally, with the condition it sounds like it's in, I'd think it would be way cooler to have as an extremely nice original example than just another MAME cabinet.
Out of curiousity, is the replacement monitor you ordered the same model as the existing one? If so, you could always recap the replacement, then swap in the (presumably) burn-in-free tube from the original...