If it were me, I'd say NO.
First ped guy we saw said that he'd probably have to extract DS's top two middle teeth, as well as an absolutely needed extraction of the two on the side of those (they were rotting away thanks to the genetics in DH and his dad's side of the family...both of them lost *several* baby teeth by them crumbling away, so for DS to only have 2 he was doing pretty good). He was also suggesting other things that made it very very clear how he had such a beautiful office, and we left his office laughing.
Found a sane pediatric dentist who filled the cavity behind DS's front teeth. Did it withOUT any sort of anesthetic; just with Finding Nemo on the TV in the ceiling to distract him. Next week with a blip of lidocaine he took out the crumbling teeth.
If you have those teeth extracted, it's going to cause a domino effect of problems for the future, as the teeth move in. And dentists REFUSE to put in spacers for little kids, to preserve the spaces caused with extractions, figuring the parents will just do braces later. When, IMO, there's the possibility of keeping that space so orthodontia isn't needed later.
I'd just say "no" to them. Make them do their jobs.
Also, have you thought of not having it all done at once? That's a LOT of possible trauma all at once. Kids are more resilient, that's for sure, but I know when DH had more than 2 fillings at once he was sore for literally months.