Definitely not necessary.
The ones in the chapter itself, yes: do memorize any of those that you don't know, because they are commonly tested.
Use the appendix only as a reference guide. If you run across an idiom in an OG problem (always study idioms specifically from official questions), and you want to learn more, you can look it up in that appendix. But definitely don't sit there and memorize them all —you won't see most of them on the real test.
The GMAT does test certain kinds of idioms frequently - most commonly, it will test idioms that do double-duty in a sentence. For instance
not only X but also Y is an idiom but it's also a parallelism marker.
Like X, Y is an idiom and a comparison marker. Those kinds of idioms are discussed in their respective grammar chapters and you should definitely know those.
There are also idioms that have to do with which type of preposition is used after a particular word —or whether you're supposed to use an infinitive verb after. For example, I have to
ability to sing is correct. I have the
ability of singing is incorrect. The problem here is that there are thousands of these in the language—you can't memorize them all. So if you make a mistake with one in a problem, sure, go look that one up. But also realize that, most of the time, the problem will offer you other ways to decide, so you can avoid that idiom issue altogether. That's better than trying to memorize thousands of idioms on the chance that you will see a handful of them on the real test.