I would have to say no.
One example, Radiology system are critical to patient healthcare. Large amount of diagnostic, specially on life threatening illness or injuries, require the use of Radiology system. The advance in Radiology technology is crucial to the delivery of health and procedure. You can't really flips thousands of images physically for a case, with potentially another thousands of priors study that are required to load and reference. Storing physical photograph media are incredibly expensive compare to storing images digitally in hard drive. IF anything. IT in this area saves the Hospital money. They don't need to hire someone to physically sort and organizes film, don't need someone to bring it to the room. Don't need someone to manages the film and flips them for the radiologist. Don't need to copy them and deliver them off site for backup. Don't need a dedicated and incredibly expensive film printer to bring to the emergency room or give to the out patient for transfer. You can just send them across the WAN, and All they need now is an IT who look after a few SANS with consumer replaceable parts.
The HIS is another. It saves the hospital money in much the same manner. Paper trail workflow are no longer needed. You don't need to expose every patient information to all staff in a binder, all they need is press a button and let the actual Doctor with the correct permission to view the data. You also don't need to store those information in paper form. Doctor don't need to waste time reading through all of them when a few keyword will produces history and allergy record or other issues. You don't need to hire people to mail or personal deliver those across campus. In fact. IT made specialized clinic possible due to the ease of moving data. Without them being digital, there are no way you can have specialized clinic that are focused on one thing. The overhead of transferring patient information would be far too great for them to handle being a small clinic.
You have to be incredibly out of touch regarding to Healthcare to think IT contribute little. IT is what made modern healthcare possible.