TL;DR: plenty of spaces @ 8am this morning.
OSM updated with the cycle parking that I could see.
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First of all, I came across about a dozen spaces before I got to the Anne Ferguson Building:
Then, I came across some more, but motorbikes were parked in them:
When I left, more motorbikes were in those spaces, and still no bicycles, so I figured that was specifically for motorbikes. Didn't see any signs, but I probably missed them.
Then, I came across a metal shed thing with loads of bikes in it:
That one was locked, so I assume it's for staff. Therefore, I didn't add it to OSM, as that would mislead the public into thinking it was available parking spaces, which it isn't.
Then up the back next to the Alexander Donald Building, loads o' spaces:
My bike's one of those. When I left, there was still masses of spaces.
So all in all, plenty of room, and this was only in the bit described above, which is one very small part of the hospital grounds. Whether it gets much busier later on, clearly I couldn't say. One would assume that around visiting hours, it gets a bit more usage.