Short answer - no. I'm afraid of spiders, but not turbulence.
Slightly longer answer - passengers and flight crews have very different perceptions of turbulence. Pilots fly every day and are used to it; what we would regard as 'light chop' would cause some passengers distress. 'Moderate turbulence' would have people throwing up down the back. I'm not afraid of turbulence because I know how strong airliners are - they have to be to withstand my landings. Turbulence has to worse than most pilots - let alone passengers - will ever experience before bits start breaking off, and airliners can sustain huge inflight overloads or damage and still land safely. Think of the Aloha 737 that lost a large part of its cabin roof, or the China Airlines 747 and TWA 727 that had serious high altitude upsets, performed aerobatics at transonic speeds on the way down, and still managed to land with various bits missing or hanging off).
That said, turbulence can be uncomfortable and fatiguing even when the autopilot is doing the flying, and we will do our best to avoid it. I am also much more aware of bumps and lurches when positioning in the cabin. I'm sure that having hands on the controls and eyes on the instruments helps insulate me from much of the discomfort.