I work with a Muslim RN who prays 5 times a day--he is discreet, and this doesn't interfere with his work. If he is very busy, obviously he can't do it. I know a Hindu surgeon who accotionally wears a Bindi--not sure why it's intermittent, I assumed some sort of ritual--and certain Catholics who wear ash in their foreheads from Ash Wednesday. My Muslim friend fasts during Ramadan as well. Many healthcare professionals modify their schedules to accommodate holy days or what have you.
We also accommodate patients needs, we have a spiritual care team. We have Clergy visit in various denominations. Occasionally, after a death, the body stays in the room much longer than is usual because of religiuos beliefs or practices. Sometimes the body needs to be washed in a ritualistic manner-we literally have to find a room with a proper drain to for the water used. Jehovah's Witnesses do not use blood products, so we use blood expander when necessary, or sadly, they are not eliglible for certain surgeries where blood will definitely be needed. Spiritual beliefs are simply a reality of the human condition.
Now as far as "praying" over a patient--well, no. Not unless specifically asked. I think offering is not intrusive either--a partient can say no--I've had many patients decline the offer of the spirtual care team.