What load(s) are you thinking of for hospital generators? Almost all technology will be fried. Maybe some HVAC systems will work but don’t expect much MRIs, catscans or X-ray equipment to have survived an EMP.
Good point. I haven’t thought through all the ways in which this would be a horrifying thing to happen.
Some of that is likely pretty well shielded or otherwise protected, by it's own nature and by the fact that it's designed to be operated in proximity to the others. An MRI is a pretty hefty source of electromagnetic pulses itself.
But of course they'd still need lights for the operating rooms and such. I'd also be worried about the back up generator's control system surviving an EMP, and the mobile sonogram systems would likely be toast too.