Apply for new H1, can i travel in June

[AnjaliK]

I have EAD and Advance Parole through Family GC processing, i am secondary applicant, my spouse is primary applicant. currently 485 is pending, due to family issues, i am filing for H1 this year as back up to my EAD, can i travel to INDIA, before/ after my H1 approves. Will it be any problem, while coming back to USA, can i still use AP document to travel back to USA.

Thanks and appreciate your advise.