I've never heard of an across-the-board feature like that for FP.
A big thing to note here is that FP isn't a straight emulator like MAME, console systems, or even VPMAME. Each table re-creation is in effect a custom emulator running within the set of physics and simulation toolboxes called "Future Pinball."
'Save state' is something you could program in for any given table in VP, and I assume that would also be true for FP. But it would be specific to that particular table.
That said, with a small amount of programming knowledge, it shouldn't be too hard to add that feature for the table you have in mind. Could be kind of a fun project, in fact.