They are not absolutely mandatory, but they can help make the process easier. Many people have CTB w/o taking AE, and several non-fatal attempts w/o AE would have been fatal if the person weren't found/called for help themselves.
I would say the most important thing for SN is the fast prior (Well, aside from the SN itself, lol). You want to have an empty stomach so that there aren't other things in your stomach to interact with the SN, or disrupt its absorption.
AE's are recommended to lower the chance of vomiting. Some people still vomited after having taken AE, and other people never vomited despite not taking them. It'll be different for everyone. Vomiting doesn't mean you will fail the attempt though. SN works very quickly after being taken. Even if it's only in your stomach for a few minutes, a lot of it will get absorbed into your bloodstream.
So as long as you're prepared for the scenario where you do vomit, then I think you will be just fine if you don't have any AE. If you have enough SN to make an extra drink(s) to take after vomiting, that's basically the best thing you can do to maximize your chances of CTB. Good luck!