I'm not aware of any such capability, but it is possible. Many large helicopters will autotransition to the hover at a desired height. Most auto hovers will descend to a desired height. The bouncy bit at the bottom would take some effort, but I see nothing that puts it out of the realm of today's computers.
The real question is will someone want this capability enough to pay for it? The limitations would probably prohibit operations from all but very open areas. Performance would have to be commensurate with the operation being flown. Failure modes would need to be proven. It wouldn't be cheap.
Cat 3 is good for aircraft on very long flights with very high eye heights that are flown in situations where saying 'no go' is costly and not understood by the customer (ie int'l air carriers). Helicopters have shorter flights, lower eye heights, and customers with a bit of fear that will more quickly accept 'no go'. Almost all IF operators should be able to accept Copter ILS minima. If not then a safe transition to an auto hover over land and then a descent to ~30 feet for a visual landing would appease the remainder.
I'm not saying it can't won't or shouldn't be done. Just that I don't think there's a market for it.
Matthew.