The lower jockey wheel on my sram mech is buggered, but I have a load of spare shimano ones. Will they fit?

You could always try it, but I think they’re a different design and not compatible.

Not done it but see no reason why it wouldn’t unless the bolt & bolt-hole in the jockey wheel are different sizes.
Strange to have ‘just’ worn the bottom jockey wheel though, I’d have though both would be knackered.
BTW BBB jockeywheels from dotbike is seemingly the cheapest option for sram mech’s, if you do decide (need) to change both.

It is a fairly new mech and the jockey wheel wasn’t worn. I swapped from my DH to my XC wheels/cassette and the chain was a smidge too short. The mech ended up wrapped around the spokes a bit, but has been straightened out. The lower wheel is in bits.