Well, at least this topic has stirred up some debate.
Another point of me looking at the Veresov is that I do play the Fantasy Caro-Kann (3.f3) and have been looking at some sort of early f3 system against the French (which this actually provides). I'm not really looking for something overtly aggressive (if I was, I would have no reason to change from my current repertoire of utter crud!), but a solid, non-theoretical system with attacking chances. From what I can see, this 4.Qd3 system, intending queenside castling and a kingside pawn storm, is almost the perfect choice in that respect, and in the case of an early ...c6 or ...e6 I would be on familiar territory.
The 1.Nc3 move order doesn't seem to have any benefit to me in most openings, especially in the attempt to reach lines of the Veresov, since it strikes me that a lot more people will play 1...c5 against 1.e4 knowing that white will almost be forced towards the sicilian, than against 1.d4 where black has to be prepared for a Benoni and a Sicilian (incidentally, I used the knowledge that my opponent played both the BDG and the Morra to play 1.d4 c5 and transpose into the latter on Sunday). I have no doubt that the Benoni is good for white, but I have no time to learn so much theory (especially since most of the best lines are quite theoretically heavy (e.g. Taimanov's 8.Bb5+ line), and also ground myself in a whole new sort of position - yes, I understand some of the ideas such as black's ...c4 sacs and white's thematic e5 advance, etc, but to understand the positions well enough to play this correctly as white would take quite a bit of study, something I want to avoid at the moment!
Alas, 1.d4 c5 2.Nc3 does not look at all promising from what I can see here, so I think sticking to the original intention of 2.dxc5 is probably best for now, or perhaps even 2.Nf3 with Lev's 3.b4 in mind... perhaps not
The point is that I'm not looking to have a 1.e4 or 1.d4 repertoire with certain bits cut out (which is what 1.Nc3 or 1.Nf3 seem to indicate to me). I'm looking to have a repertoire based on the Veresov, which is totally separate to the 1.d4 and 1.e4 complex proper (as I see it anyway). The only lines that black can transpose into after 1.d4, 2.Nc3, 3.Bg5, 4.Qd3/4.f3 are lines I already play, or lines I'd be happy to play (such as 3.e4 vs the Pirc, or the Caro-Kann/French lines).
Thanks to everyone for their feedback.