You could do this, but it could raise questions of whether the initial job offer from the labor certification-sponsoring employer was valid. Employment-based green card applications are all based on the concept of a future job offer. Therefore, there is no legal requirement to work for the sponsor at the time of filing the labor certification (LC), or even while the I-140 or I-485 is pending. 

The best proof that a job offer is valid is working for the sponsor. Thus, filing a case as a future job offer, without working for the sponsor, then using AC-21 to move to an alternative position, can raise questions of intent and potential fraud or misrepresentation. The safe approach is to avoid this scenario by working for the sponsoring employer.