It is possible. You will have to work with both the CNC and CMM vendors and your EE to determine how best to handle this. Most CMM's can't do record keeping / spc / averaging so this is best handled in the CNC via macro or by a separate SPC computer that feeds info to the CNC. You do not want an adjustment for every measured part, you want some moving average and you need limits on the adjustment amount.
For instance, if it measures 0.008 mm from nominal, and your tolerance is +/-0.100 mm, do you really want to make an adjustment? - probably not.
If you get a reading of 1.3mm from nominal when the tolerance is +/-0.100 you don't want to make an adjustment then either. So there are lots of things to think about.