Why not? People sue for everything else in this universe...why not add turbulence to the list.
She wont have to prove the pilots were careless and reckless in the operation of that flight. She just has to be a big enough nuisance to United to get a payout.
You would really hope the judge would throw this out as frivolous but past precedent in other ridiculous lawsuits will likely prevail and take this one all the way.