At times, yeah. The closer you get to capacity the more the staff are overworked, the more likely you are to be attached to the old/cranky/unreliable ventilator, the more likely you are to be seen by fill-in staff pulled from other departments, the more likely it is that your hospital will run out of some medication and have to substitute, etc...
So all other things being equal, you'd expect CFRs to rise with case load. Probably not linearly, but measurably.
