There's lots of reasons why it would be silly, pointless, and probably detrimental. First of all, if marriage exists without government recognition, then technically gays can already get married... they just don't get the same recognition for it. The reason they don't just get married without it being recognized is that this would be absolutely pointless - the whole reason they're fighting is to get the same rights as everyone else, those rights only existing because of the recognition of marriage. The point is that if the government had a "separate" "civil union" that wasn't marriage, it would be all that would actually matter - and not actually calling it marriage would probably have some ill effects as people become uncertain of what exactly marriage is. It reeks of opportunities to sort of cheat the system and get a "union" purely for the benefits it reaps, for one thing. You'd also have a lot of confusion about which type of "union" really mattered, family-wise... which would not bode well for those with one, but not the other.
Granted, that's assuming that it would be any different from what exists now, which I don't see how it would be. Again, it's already possible to have a "religious" marriage without government recognition... it would just be completely pointless to do so, so nobody does it.