I understand coming on here to get a feel before going further, but don't just ask tatoo artists. Ask a real doctor. You can still go through any procedure that requires an epidural (it's not just labor), but you need to use alternate methods of pain relief.
A boss I used to have had an ink injected into her blood stream as part of a procedure and her doctor DID tell her she could never have an epidural again. She was 63 so the chances were pretty limited that she'd need one, but it still tells me it's worth asking.