If neither Brown nor Schwarzenegger chooses to appeal the case, and no law requires that they do as far as I know, then an appeal by the people who helped put Prop 8 on the ballot and get it passed isn’t an appeal by the state and that by itself could be sufficient grounds to dismiss the appeal on the grounds that it was not brought by a party with proper standing.
Assuming that the state continues with its salutary decision not to defend Prop 8 in court, the question of whether Prop 8 supporters could have standing to appeal the ruling holding it unconstitutional lands squarely in a doctrinal gray area. To oversimplify only very slightly, a higher court will be able to grant standing if it wants to do so and refuse to grant it if it wants to do so. It’s possible that the 9th Circuit could see a refusal to grant standing as a “minimalist” way of avoiding a difficult issue, and perhaps insulating a decision they like from immediate Supreme Court review. As a means of keeping Judge Walker’s decision away from the Supreme Court, a refusal to grant standing would only be very temporary. As long as there’s a federal precedent holding that bans on same-sex marriage violate the Constitution there will be a flurry of lawsuits in other states, and the Supreme Court is going to step in, probably sooner rather than later.
Having said that, kicking the can even a little bit down the road would be good for proponents of same-sex marriage — as long as same-sex marriages are permitted to go forward in California. The more Californians that have legal same-sex marriages and the longer the right remains in force, the harder it will be for Kennedy and other moderate conservatives who aren’t entirely hostile to gay and lesbian rights to vote to rule same-sex marriage illegal. Going forward, then, the most important question may not be whether the 9th Circuit finds standing but whether it chooses to stay Walker’s ruling.
UPDATE: More here.