Does an applicant of E2 visa living in US have a right to run on own risk a business before getting an approval from USCIS on E2 application?

In past I was always starting to work on H1 after applying to USCIS but before getting an approval.

Is same practice acceptable with E2?

In other words can I do the following?
Apply on Feb 1 to USCIS on E2 and on Feb 3-4 start running/working in a new business, described in application to USCIS?

Can you please accompany an answer with a source?