It could. I get the impression tech is pretty accepting however who knows your future path?
One of my kids had an internship at a nonprofit that did not allow visible tattoos, and this wasn’t a super uptight place but a place where employees interacted with the public.
Why close any possible doors if you don’t have to as you never know where your future would take you. I’d stick to places that can be easily covered without having to wear clothing to your wrists all the time.