Nope, they will only set as many as they are going to set. Triming off the spent blooms won't make any difference. I saw a number of wild ones a while ago but can't remember where.

From the time that I went into the service until I got out sunflowers had become a big cash crop in South Dakota. My dad had planted 320 acres of them, which is one mile by a half a mile. That's alot of sunflowers. I couldn't believe, after years of fighting the d*mn things we were raising them. Take care, Bill.