Yes, easily. In the capability analysis dialog within Distribution, you'll be able to choose a distribution for the data. Normal 2 Mixture is an option.
Are you using JMP pro, or maybe it is a new feature in JMP 14? I'm using JMP13.2.1 standard and I don't think I have that feature.
My two cents on the topic is that if I care enough about a given parameter, I would make sure I understand why the distribution is multi modal, understand how close the modes are to one another, whether they're stable, and decide whether it needs to be or can be "fixed." If not then I'd apply some robust stats to it. For example either JMP's robust mean / standard deviation to get a robust cpk, or use a function of median and iqr to do the same.
I'm using base JMP version 13.2. You can also get the capability analysis for any of those fitted distributions by clicking the red-arrow icon for the fit and selecting "Spec Limits". Setting those will generate a capability analysis.
If the normal mixture model is a valid description of the data, then it implies that there is more than one normal population. What does it mean to ask if they are stable and capable as in the case of one population? That they are individually stable and capable? That the mixture of the two is stable and capable?
Why is there more than one population? Can they be identified?