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roe is correct and PhilDAS' advice is worth following (or email them). I've fitted a Pistard Air to a Pursuit Champion, which has a slimmer/tighter rear end anyway, and there's approx. 10mm of clearance between the chainring tabs of the spider, or approx. 12mm at the end of the crank arm, and the chainstays.
The chainring tabs on the Pistard Air aren't as porky as they are on the Omnium (IIRC), so if you did get one of the Omnium-incompatible frames, the Pistard Air would probably just about fit. Still, best to contact them and try to get one from the latest batch, that definitely will work with both cranks.
Anyone know if the new Pre Cursa frame, that according to the site no longer fits Omniums, would accept the Miche Pistard Air? I think @Lukas you were asking for the same reason? Not sure if its the external BB that causes the issue on the newer frame or another property of the omniums