I _think_ if you have applied for Premium Processing and get the receipt, you can start working with the new employer. But please check with your employer's lawyers, as these things can keep changing and the rules are too complex for me to keep track of.
The lawyers have not mentioned anything near that, otherwise I'd be working right now!
My application used Premium Processing, and I got an RFE, so I'm still sitting here on my hands. It's frustrating, but is it worth asking the lawyers about being able to start since I'm in the process of the application?
Nearly every lawyer will encourage you to wait for the receipt notice, although interestingly you only need proof that you've submitted a petition to starting working; i.e., a Fedex proof-of-sending receipt.