Depends on state laws. Best practice in TX is to carry a copy (or picture) of your stamp. Show it to the cop when asked. Most cops would leave you be.
In Texas though the stamp is just a "defense to prosecution". Which means an NFA firearm like a machine gun or SBR is still a "prohibited weapon", you just have a pre-emptive defense to being prosecuted. So you can still be cited even if you have a stamp, your ID, your trust, etc... Because think about it...how is some beat cop going to know if that stamp is real or not (especially if you have the digital one from an e-file)? They won't be able to determine that. So they are given the leeway to issue the citation, and the city/county/whatever who would actually bring charges checks the validity of the registration before prosecuting.