I am a U.S. taxpayer employed overseas. I file a Federal Return and a California Nonresident return only (under the California safe harbor provision). Does TurboTax support this? It seems to want to insist that I be a Resident in at least one state.

Yes. You should have a foreign address. The safe harbor allows you to file as a non-resident and make an adjustment to your CA wages to report your taxable state income. 

Thanks! That's good to know. But I don't have a foreign address, I have an address in the APO/FPO/DPO system. Does that work?

Under Personal Info, you can go to Edit on the Summary page and indicate that your state of residence is a foreign country or US Possession.  Then when you enter your address you can choose the drop down for APO/FPO/DPO.

On the Summary page you can also edit the question:  Other State Income and indicate that you have to file a California return.