It would probably do so by advocating against the policy in the public forum where their employees weren't specifically targeted as the audience.
I think the meat of the issue is that Uber doesn't get to decide Prop-22, it's a decision by California and if you want to sway CA talk to CA. If you legitimately think your business and all it gives to the economy and community would be destroyed by that proposition then tell that to all the residents of the state - targeted messaging to your employees is just all sorts of shady and, whether intended or not, it will leverage the power imbalance of the employer/employee relationship for some people.
It's pretty much the same reason you should look elsewhere for love - there is an existing relationship between an employer and employee - bringing other relationships into the scenario just makes things murky.