Is it safe to say that memorization is a necessary part of playing the Sicilian?

I started learning the Najdorf and it seems that I wouldn't get anywhere without having to memorize some lines--some of the tactical maneuvering would be extremely difficult to see OTB.

Well the opening is fairly simple for it, and memorization is fine until someone throws a curveball, but usually that is a mistake then.  I'd say that understanding of tactics and strategy is FAR more important than memorization.  You can only memorize so much for so far before things start to get muddy.  Therefore yes, you can memorize the first handful of moves, but what happens when your opponent does something different?  You have to adapt.

Najdorf is one of my goto responses for e4.

It is safe to say that all memorization must lead, not to further memorization, but to the negation of memorization, a return to the point of departure.

a la Eugene St. Croix

(one of my favorite Romantic Period artists....) 

Maybe it is easier to understand and follow some lines once you have the experience you get by playing the opening. Thus a mixture of playing and in between doing some study could be rewarding.