No, it's silicone it just bounces back. The nails you work on are removable/replaceable so it can't be attached like living tissue.
Cuticle work should be gentle, letting cuticle removing products do the work, tools should just be removing the debris, not scraping or pressing too hard. Do it to yourself, watch how much pressure you apply to yourself and how firmly you press, then replicate that on clients as a starting point. Also remember not everyone experiences pain or discomfort at the same level, what hurts some clients will barely register with others. Have the confidence to press as firmly as you need but ask the client whilst doing the first finger if that pressure is OK with them. The trick is to ask the question in a way that they can say it hurts without thinking they will offend you or feel like they are complaining. I say 'cuticle work feels a bit weird but shouldn't hurt...how is that for you?' They'll either say 'no it's fine' or something else, this is when you listen carefully to what they say and take your lead from them adjusting pressure as needed.
I have a couple of clients who love it and ask me to do them all again
I have one client who absolutely loathes it, her feet fidget and she tries to twist her fingers away the whole time. She's been coming for years, I've proven the need for it so we have agreed now that ignore her fidgeting, hold her finger tightly and just get on with it and get it done as quickly as possible.