Can OPT and H1B apps on file with USCIS at the same time?

I am graduting soon (Dec. 15). My driver's license will expire at the same date.

My future employer agreed to file H1B premium processing for my H1B (non-cap) starting at Dec.15. But up to now now, they still have not filed my H1B application yet.

I am considering apply for OPT then I can get my I-20 extended and use it to apply driver's license. I will have a lot of travel after my graduation. At least, I need to move to where my future employer is located.

Can anybody comment on whetehr I should apply OPT, when would be a good start date for OPT? If I apply OPT now, weeks later, my employer files H1B application, am I having the risk of be denied OPT or H1B application?