You can get sore knuckles/fingers, yes. There's a number of things that can cause this. First the infamous "death grip" of pole newbies. Let's face it, our instincts are to hang on for dear life when in fact we don't need quite as much as we think. As you become more experienced two things will happen, 1) You'll relax more and not hang on quite so grimly 2) You will become naturally stronger anyway and need to put less effort in for the same, if not more, return on your grip if that makes sense.
It's important your body has rest days. In the beginning it is not uncommon to need a lot of rest days between sessions. A person is often unfit and weak. This means that you tire more easily and your body just isn't as strong, flexible or adaptable so your recovery rate is very low. When I first started I was still sore four to five days after, it was insane. Now I do not suffer anywhere near as much. I know it's tempting to train train train like some crazy pole bunny in the beginning but don't do it. Resist the urge. You will be setting yourself up for injury, slow down your conditioning and put extra strain on your body. No one has ever regretted going too slow, plenty have regretted and paid the price for going too fast. Times of rest and recovery are vital for the human body no matter our fitness level or spot.
Another thing, keep an eye on your alignment throughout your wrists and ensure you are engaging your shoulder muscles. Not doing so can put strain on various areas of the body. Make sure you stretch out your arms, shoulders and neck after every pole session. It's crucial.
