It doesn't increase ticklishness directly, per se. But it will put you on edge and make it more difficult to relax, which might possibly raise your vulnerability somewhat. A lot of being ticklishness is not just the sensation, but the fear factor, the uneasiness, and the dreaded anticipation. That's why people often giggle and squirm just from somebody wiggling their fingers in their direction.
Many ticklish people will tell you that their ticklishness depends on their mood. If they are in a relaxed state, they can often just absorb the sensation without reacting to it. Somebody who is going through nicotine withdrawal has a significantly slimmer chance of achieving that relaxed state.