Hello Dr. Cherny, I can email you a document (if you are interested) scanned from the Ed Bruce files at NARA, College Park, that addresses this question relative to the PWAP.
The Southwest regional director of PWAP, John Ankeney, apparently commissioned artists as long as they weren't employed full-time (according to artist Everett Spruce--see Francine Carraro's bio on Jerry Bywaters, p.83).
As for the FAP, I would assume there was a means test of some sort since it was administered by the WPA. Per the "Final Report on the WPA Program (pp. 15-16):