No, it doesn't. Government can and has previously 'contracted out' to religion to provide the definition. You would remove religion from that and place it squarely in the lap of politicians.
Which do you think would be more honest, moral, and just about that? Think about it.
It would be best if government simply stated that it grants recognition to whatever religion declares as marriage. Period.
As religion doesn't recognize marriage between gays/lesbians, then neither will the government... *AND* they will not have the vested power to change that (see above paragraph).
You can't be serious, can you?