Travel on OPT while H1B Approved

I am currently on OPT working as a lecturer for a reputed university. My OPT is valid until August 16, 2017. My employer has filed Cap exempt H-1 B for me and it was approved today. My H1-B is valid from August 16, 2017.

I need to travel to India in the month of May. So I am planning to make an appointment for H1-B visa stamp in May. Since my H-1 B starts from August 16, 2017, Can I travel back to USA on Jun 24th on my OPT Status? I have a valid F-1 visa and I-20. Please let me know.

Your prompt response is greatly appreciated in this regard.

Why do you want to get H1 stamped in the first place, when there is no necessity for it ? Travel and be back on F1. Get H1 stamped on your next visit after your F1 visa expires.