It may irritate them, as whatever you use to lubricate probes does leave some internal residue, at least for a little while. I wouldn't do it. Just use a water-based jelly like K-Y or the generic equivalent.
The stainless probes themselves are super easy to keep clean. Wash them in hot soapy water, scrub with a paper towel, rinse off the soap, good to go.
Also, if you have not probed before, it really, really helps to see it done in person and have someone guide you through it.
