Please expand your question. Are you asking whether any drug could accomplish this? If you consider full anesthesia, it would seem the answer is yes. If you are asking if drugs in the same class as lidocaine could be used to deaden other senses, I think it would depend on where they were administered.
Obviously. It’s not like my whole body goes numb from the dentist’s injection, no?
But I wonder how it would work on nerves other than those that transmit signals of pain or pressure. Like, say, the ones mentioned: optical, olfactory and auditory. Would lidocaine deafen other senses than the purely tactile? If it were injected close to said nerve, and in sufficient quantity, that is.
Lidocaine inhibits the general mechanism of neural signal conduction, so in principle you could do what you suggest. But you’d have to deliver the lidocaine specifically to neurons somewhere between the sense organ and the brain, or into the appropriate part of the brain itself. For eyes, ears and nose I think that would be physically difficult, and I can’t really imagine any therapeutic motivation to develop safe techniques to do it? Injecting anesthetic in or near the brain might not do permanent harm if it didn’t affect the autonomic nervous system, but I wouldn’t volunteer to be a test subject.
There’s a fair amount in the literature about sensory loss as a complication in anesthesia. The most common appears to be hearing loss from spinal anesthesia, but it appears that it’s probably not neurological.
You can find literature on experiments with rats, for example:
But there are easier ways to disable a rat’s senses if that in itself is required for experimental purposes.