Travelling to US during pending naturalisation app

I applied for naturalisation on 18 July. From different timeline threads, I have gathered most applications are taking from about 3 to 6 months.

My husband are travelling to the US end of October. What if my decision comes through before we fly and I need to send back my BRP within the usual timeframe? Can anyone please advise if I would be able to reenter the UK without my BRP?

Travelling while awaiting citizenship is absolutely fine. 

What will happen is you'll receive a letter inviting you to a citizenship ceremony (I think you have three months to have the ceremony), then after your ceremony you need to apply for your first British passport before travelling.  So you have a lot more freedom over travel while citizenship is taking place.  You'll know to wait to schedule your ceremony until after you've completed travel.