oh rando!, i'm on your side! (well, not of the atlantic obviously, but you know what i mean.)
but in answer to your question, i'm presuming the PBP is something you plan for, rather than just 'nip' to on your way home from somewhere. Therefore i would think it pretty nonsensical if the journey from home to the start and from the finish back home again is more of an influence on bike choice than the actual ride itself, particularly when the only vehicles you can't take a normal bike on are some buses. Trains, planes, automobiles - you can take bikes on all of those.
Could I ride anything over it? probably, although i never have done as yet. I can't see any reason why not, can you? (presuming by 'anything' you mean anything *of my choice*, rather than anything as in any given thing you care to think of)