The cord and plug connection cannot be above the dropped ceiling, so you have to mount it face-down, in the ceiling. Your fixture's cord and plug was part of a UL listed assembly or luminaire, so I think you created a violation when you didn't install it per the manufacturer's intended method.
Of course you can have cord and plug connections in patient care areas. The headwalls are full of receptacles. IV pumps and monitors of every sort get plugged in. Heck, the last time I was in the hospital, I had them bring me a fan (that plugged in
) to drown out the noise of my roommate who made all sorts of funny noises during his recovery.