Short answer, Uh yes! Skin penetration with sharp objects can be quite painful. Long answer, No. . . it is all going to depend on YOUR pain threshold, where the tattoo is going, how big or small it is and how long you are sitting for.
Most painful areas are said to be those with a lot of nerve endings, close to the bone without much fat, or where your skin is quite thin.
Least painful areas, think the opposite to the most painful, where there are less nerve endings, away from the boney bits with more fat and the skin is tighter.
There is no way to really gauge how much pain you will or won’t be in, it all depends on you.