I don't know how serious a campaign Swearengin will run but if she runs a serious campaign she has a chance. She won't be running against an incumbent. Democratic incumbents are impossible to beat here but open seat races are ones Republicans have a chance in. She'll bee running against a Democrat with a decent profile, but who isn't well known statewide. I'd guess that Betty Yee isn't well known outside the Bay area and that John Perez isn't even that well known in Los Angeles. I pay attention and wouldn't know where his district is without looking it up.
Swearengin is coming from the Central Valley, an area with a big Democratic registration advantage, and one that voted heavily for Obama. But it supports Republicans down ticket. In 2008 she defeated now-Assemblymember Henry Perea for mayor by a margin of 12,000 votes, while Obama was beating McCain by 21,000. Perea is now considered the Democrats best Central Valley hope to beat David Valadao in 2016.
Swearengin will make top two without spending a dime. If she does a little work, the primary electorate could even give her 50%. In 2010 the two Republicans pretty much equaled incumbent John Chiang's vote total. The primary should deplete the bank accounts of the Democrats, however. So she'd start a general election on equal footing.
Some people might scoff at the idea a Republican has a shot. If you look at open seats Republicans ran against candidates who hadn't won statewide before, their record shows they've been close. In 9 such elections between 2002 and 2010, Republicans lost the 5 of them by 4 points or less and two of them by less than a point. Strangely, the one open seat a Republican won was the 2006 insurance commissioner race that Steve Poizner ran against the incumbent Lieutenant Governor.
Swearengin is certainly an underdog for November. That electorate will likely give the average statewide Democrat 57-58% of the vote. Yet if you're betting one race will be tight it could be this one.