Yes. I donated platelets (aphoresis) for ten years (two needles, two hours, twice per month, a double-volume). A few years after I started donating, my state became shall-issue. I discussed carrying with my technicians/phlebotomists and carried from then until the American Red Cross posted the facility against legal gun carry. My protests were ignored but I never darkened their door again.
They prohibited even cops from being armed while donating, supposedly for fear of them losing control of their gun while faint from donating blood. Phoresis does not cause a volume change nor syncope.