Can someone without "H1B Status" but has a approved I797 and H1B Visa transfer? Or can an individual with a H1B Visa and approved I797 petition with current employer transfer his/her visa to a new employer obtaining a new I797 petition for new employer with being CAP exempt and without entering the USA on this H1B yet?
Yes, that is possible, once your new H-1B is approved by USCIS and you'll want to travel to the US with your old employer's visa.