Anything is possible, but..
Access is a sticky situation, to say the least.
Getting equipment down there, diving and getting equipment out again would be a several day event.
You'd need the Grosvenor Caving Club to sort out their access agreement; some means of getting the equipment down 400ft of rickety ladders (some of which need replacing, I believe); to move the stuff about a mile through knee-deep water - and then you'd be there. And then repeat in reverse.
The pool itself is rather interesting, in that it had rubble dumped in it for many years, with no sign of it filling up - it might be very interesting to find out more about it, but it's possible you'd need to be equipped for some seriously deep diving...
Hello again darkness, my old friend...