If the STOP campaign collects enough valid signatures, there would actually have to be TWO votes, not one, to stop the arena. The first vote would be on the issue of whether or not funding for arenas has to go on the ballot. If that were to pass, then the second vote would be on whether or not to fund the arena. There are some procedural questions about whether the signature drive is even valid, on top of that.
But even if it went to a vote and the first vote went STOP's way (which I could see), I truly believe that there is no way that the second vote would go poorly. The community appears to support the arena by a large margin, with only a very small contingent of people supporting STOP. Recall that in order to get enough donations to run their signature campaign, they had to get money from ulterior-motive-man Chris Hansen, and that they still needed to be misleading (e.g. "Sign this petition to support the arena") in order to do it. There's just simply no groundswell of support behind the dozen vocal naysayers, and if push comes to shove, the facts of the city's contribution come down squarely on our side. In the end, STOP would be forced to either continue their outright lies about the size/nature of the city's contribution (and they'd get absolutely hammered on those lies by CrownDowntown and others) or concede that what they're really fighting against is an arena that, outside of a $38M land contribution (which said land actually can't be sold for $38M today because of the Natomas building moratorium) is completely financed by the investors and the arena-going public via fees and parking. The city's general fund essentially acts as a backstop to guarantee the payoff of the $212.5M in bonds, but that's only if revenues fall short. And even then, if revenues fall short a whole $1M per year, the city isn't on the hook for the whole $212.5M plus bond interest, it's on the hook for the $1M per year...$35M total in a pretty worst case scenario. And even in that worst case scenario, that's $38M of land and $35M - $73M total - for a downtown arena and all of the surrounding development and revitalization that it will bring. Cheap at twice the price. And that's what STOP is fighting. When people see that, they'll know the right vote. So don't panic.