Yes and no. More accurately, yes, but it's not easy, and you can't do it for a single trial -- you need many trials.
You first need a fairly good biopotential amplifier, with surface electrodes on the skin surface above the nerve that carries the signals to the spinal cord. This is the easy part.
Next, because the signal is tiny and noisy, you will never see one event, thus you need to do this hundreds to thousands of times, and average all the events to see it. This is called ensemble averaging. This is a killer method for pulling tiny signals out of noise.
When I was an undergrad, the lab I was in did this in rats, looking for cells in the spinal cord that responded to both renal nerve stimulation and somatic sensory information (Knuepfer et al., 1987 --
https://www.sciencedirect.com/science/article/pii/0006899388912929 ). We glued a pin head to a small speaker cone, and put the pin head near the skin. We could poke the skin by sending a signal to the speaker, and use the same signal to trigger acquisition. We had the advantage of recording single neurons, so we didn't need to average for very long.
(Historical note: IIRC, we had a fancy homemade ensemble averager, and I have no idea what the mechanism was. More conveniently, we used some custom hardware to generate inputs to an analog storage scope that displayed the output of a window discriminator as a raster, as you can see from the snip from the paper referenced above. Z-inputs on scopes can be a wonderful thing!! The scope screens were simply photographed using an oscilloscope camera with Polaroid film, and then the graphic artist would generate the figure using special high-contrast film to generate a negative image -- NOT the way it's done today)
Each horizontal line of dots in the image is a trial, with a dot showing the occurrence of an action potential. We could see this because we were recording with very high impedance electrodes right next to the neuron. The data would be much less clear (and, in fact, for this case, not possible) with surface electrodes. You might be able to see the story from one sweep line, but when you stack many trials right on top of each other, it's a very loud story. For signals using surface potentials, you really would need to average to see anything.
In my bioinstrumentation class, I do a demo with electrical stimulation of the medial nerve at the wrist, and record from where the nerve enters the spinal cord near the neck with surface electrodes. You can get a response sufficient to measure nerve conduction velocity, and show that there are different types of nerve fibers by their different speeds. This is done clinically, in EMG labs, using similar methods, but with electrodes that break the skin for better signals. They still need to average. These systems are commercially available, in the thousands to tens of thousands of dollars range--e.g. https://mfimedical.com/products/nicolet-viasys-viking-select-emg-ncs-machine1
You should be able to do this with a modern digital oscilloscope, most of which have some sort of averaging facility, if you have a good trigger signal, and if the averaging routine allows you to use enough sweeps.
The last part, the yes/no answer, is trivial compared to the rest, but useless until the rest is handled.