Absolutely! They should also be on Hatzolo. When a woman in labor calls Hatzolo, and they have to assist in a delivery, no man belongs on such a call. & specialty fields of women’s diseases & issues, should most preferentially be dealt with, by a woman Dr.
Having a Hassidic guy assist a woman in a delivery, is worst than an unfiltered computer, to say the least, especially when there are qualified women personnel around.