I know nothing about powered-lift aircraft, but according to 14 CFR 61.5 they're a separate category for licensing, like airplane, rotorcraft or glider. It is therefore possible to get a "private pilot powered-lift" certificate without having any flying experience in any other aircraft type. 14 CFR 61.109, 61.129 and 61.163 state the flying requirements for private, commercial and ATP powered-lift ratings respectively and 61.65 has the requirements for a powered-lift instrument rating.
61.109(e)(5) does allow substituting some limited airplane (i.e. fixed-wing) experience for powered-lift time:
(5) 10 hours of solo flight time in an airplane or powered-lift
consisting of at least—
There are also allowances for using simulator and military experience in lieu of powered-lift flight time, but I couldn't see anything that directly allows rotorcraft experience to count towards powered-lift certification. The fact that powered-lift is a category of its own suggests that the FAA considers them to be significantly different from rotorcraft.
So yes, you could theoretically start from zero and work to get your private, instrument, commercial and/or ATP ratings with flying time in powered-lift aircraft only. If, that is, you can find a powered-lift aircraft and an instructor: an ATP requires 1500 hours of experience and doing them all in powered-lift aircraft may not be practical (61.163 only requires 250 of them to be in a powered-lift aircraft).
In reality, I suspect that any civilian powered-lift pilots who are not ex-military are (or will be) people with extensive rotorcraft and/or fixed-wing experience who then follow a training program provided by the aircraft manufacturer. Your insurance company will probably also have a say in who you hire and what experience they have.
Finding and training those people won't be cheap, but if you're buying up new AW609s then you can probably afford it :-)