I guess that's a pretty old picture in your avatar then.
Yeah, no, that's not how it works. The majority of the time, finish one bodypart before moving to the next.
Norton is smarter than you and I combined. If you're going to do his plan, it would be retarded to drop one of the leg days.
I wouldn't necessarily call you "small" like you should avoid an arm day. Some people have a days for just arms and some do fine just training them as part of other workouts. As long as you're training them, and training everything else, it's not a major issue either way.
That program would also be pretty good. I'd tweak the sets/reps on the upper hypertrophy days (I don't see the point of exercises in the 5-8 range on those days); I'd train chest before shoulders on the push day; I'd drop lunges from the lower strength day; and I'd swap the incline DB press for some kind of overhead press on the upper strength day.
I'd probably also try to swap the two lower body days during the week, so you're not trying to squat and deadlift heavy the day after rowing heavy.
As long as you're eating enough and training with a decent plan, you should be able to see the results you're after.