Student Visa (F1, F2, M1, M2)

Hi,

I am an international student needing some advice on travelling outside the US. Here is my current situation –

I am working on my OPT (F1 student visa)
My company applied for H1B petition this year and my application was picked up in the lottery. I think it’ll be effective from October onward once appoved.
But I am planning to leave my company in coming June and join another University in August for graduate school.
I was told that my OPT would end as soon as I transfer my i-20 to my new university so I waiting until June to leave my company and then transfer my SEVIS and i-20 record from current to new University.
 

My question is – Can I travel to India in July (after leaving my company and before joining my new graduate school)? I would have transferred my i-20 by then so I’ll have the new i-20 from new University to enter the country. I understand that having new i-20, I shouldn’t face any problem entering US but I am afraid that having my name in H1B petition has made it trickier. Under the petition, I am asking USCIS to convert my F1 to H1B so technically my F1 is no longer acceptable to re-enter the country, is that true?