To answer your actual question, no, the pending H-1B application should not affect your travels.
According to this website, here are the minimum requirements to re-enter the United States on F-1 status:
- A Form I-20, endorsed for travel and signed by your DSO (designated school official)
- You have been out of the United States for less than five months
- A current passport valid for at least six months after the date of your reentry or, if you are from one of the countries listed below, a passport that is current through the date of entry
- A valid, current visa or you travelled to contiguous country or adjacent island for less than thirty days
- Financial information showing proof of necessary funds to cover tuition and living expenses
Please note the requirement for a valid, current visa. Your initial visa got you into the US in F-1 status, which you're still in. If the visa has expired, it will not get you back into the US if you travel farther than Canada, Mexico, or some Caribbean countries.
Another FAQ says that the Department of State suggests that you apply for another visa from your home country.
Yet another possible gotcha is whether you'll have graduated by the time of travel. That could mean you're out of F-1 status and into the 60 days you get to leave the US. You will likely not be able to re-enter.
Will you be on OPT (optional practical training) or have applied for OPT at the time? Then you should have your EAD (employment authorization document) and letter of employment when re-entering the US. If the EAD was pending, it'll get sent to your US address.