Travel during COS H4 to H1

I am on h4 visa and working on EAD. I was on H1 earlier and now my employer re-initiated my H1 couple of weeks back, still waiting for my receipt notice. I want to go to India for few weeks (end of May to mid of June). Can I travel during COS and continue working on EAD after I came back? If I got my H1 approved do I need to go out of the country for stamping? If I have to apply for COS, can I still continue to work on H4EAD?