The chance is really low, I simulated about 1million trials (of 100 rolls from 4-7), and it is about 5 had 600 or higher as the total. So about 1 in 200,000 chance.
Another option is to assume normality (Gaussian distribution):
X = {4,5,6,7} with 25% chance each -> Mean = 5.5, Variance = 1.25
Call Y = X1 + X2 + ... + X100 (aka, 100 independent rolls of X)
Y mean = 550 (100 x 5.5), Y variance = 125 (100 x 1.25)
For a normal distribution to be > 600, with mean= 550, variance = 125, this has a chance of 0.999996128 which is a 1 in 258,257 chance.
So basically if you were able to try this every 20 seconds, you will be waiting for about a month or two to beat it with just air dice.
