You can skip over the two theorems (3.5-1 and 3.5-2) in this section.
What you do need to know are the formulas summarized on the Discrete Random Variables handout: p.m.f., expectation, variance of a Poisson distribution, and the exponential series formula. As with the binomial distribution, when working problems involving the Poisson distribution, you should not use tables for this distribution (as the book does in Example 2.6-1), but work solely with the formulas for the p.m.f.
All I can advise you is to wait and see if spaces open up. This frequently happens during the first few days of the semester due to dropouts. In fact, in past years there have always been enough drops so that everyone who wanted to be in this class could (eventually) be accommodated. As a backup, you might want to sign up for a section of Math 461, the regular undergraduate probability class.
Note that in order to be able to register for this course, there must be spots available in both the lecture and one of the discussion sections. If there are spots available in the lecture, but both discussion sections are full, you will not be able to register.