The short answer is No. It doesn't appear to.
I spent Christmas day loading 100 rounds of 300 AAC Blackout with Speer TNT 125 grain bullets. Using a Hornady Bullet Run out Gauge I ran the run out on each cartridge before and after crimping. The average runout was +/- .001 to .0015 inches. This didn't change with moderately heavy crimping -Which is to say it neither got worse nor improved with crimping. I used shortened Federal 5.56 brass that was FL resized, trimmed, had the case mouth flared to accept the bullet base, and then seated. The Dies were Lee and the press was my Forster. A Lee FCD was used to crimp.
As a further aside on the necessity of crimping properly, I read an astoundingly unscientific article on reloading for the 300 AAC Blackout by the NRA here in the US. The author reported poor accuracy using a taper crimp from the Redding dies he was pimping for the piece; writing off poor accuracy with bullets such as the Nosler 125 gain Ballistic Tip to the lack of a crimping groove. I have loaded these same bullets with identical loads as his but used a Lee FCD and got half MOA. Save the taper crimp for light loaded 45 ACP or 44 Special gallery loads...~Muir