YKA

I would let the masters weight in, but while you are waiting for your NOA2 I think you would be ok to renew your passport. 
You can also communicate to NVC once you get your new passport number, and send a note to inquiry while inquiring about your case number. 
At that time you can also tell them to update your email, and inform them of the passport renewal and change. 
I would think you would want all of this done before you get your case number assigned, and start creating your next package that you will send to your beneficiaryfinace'
My fiance had to renew her passport, we just brought both into the interview and had copied of the old and new and mine. 
You would use updated information as you still need to file your DS160, pay your visa fee, schedule your appointment, get your affidavit of support together, etc etc, 
Lots to do. 

Renew it now before you need to fill out the DS160.
 
Good Luck!

I renewed mine after filling out the ds160 and it was no problem, they probably see it a lot. i am unsure about renewing before your noa2 though. 

I would renew ASAP if you aren't planning on traveling. Last thing you want is leaving it close to interview and experiencing unforseen delays on receiving your new passport.
 
Just be sensible about this. Many have renewed even after ds160 but their experience is their own and there's no guarantee it will be as smooth for you. Timely preparation will be your best friend during this process.

Had no problem with my renewal. I think it was around the DS160 (it's been awhile). I had my new passport issued with a note stating it's renewed/replaced the previous number. Consulate officer thought that was pretty slick but could not have cared less.