I don't even know if the racers could even bring a dynamic(moves the tire under its own power) balancer if they wanted to.And, are their tires made to the exact same specifications as our street tires? I don't think so.
I don't know what the limit of facilities are, but the guys changing the tires are doing so under Michelin, Pirelli, Dunlop and other banners, with fully functioning Coates changers, so whether or not they could use a dynamic balancer if they wanted to is a good question. I might ask next time I'm up there.
But now that I think about it, why would accommodation not be made for this type of balancer to be available if a quantifiable benefit could be realized? They seem to spare no expense for any and all pursuit of perfection, sometimes with questionable merit.
Just to clarify, I haven't seen racers doing their own at the track, though I've been known to change a few for a friend between race weekends, so I'm sure many of them do their own as well.
As to the specs of race vs. street tires with regard to balance...the last set I changed and balanced was for Radman; they were the new BT 021's and took less than two squares front and rear. Most of the well-known name brands are remarkably well made, and if you take the time to align light and heavy spots on the tire and rim, use very little weight.
Usual use of weights at the track are in the 2-3 square range per tire. They don't take the time to align light spots and heavy spots, but the lead weight tape residue usually shows up on one quadrant of the rim, indicating relative consistency of manufacture quality.
Good stuff,
Shane