It is not necessary, but recommended.
AE products do not guarantee that you do not vomit.
You can still vomit, so even if you take AE, be ready for vomiting.
Without AE, you definitely have to prepare for vomiting.
But the lack of AE does not automatically mean failure.
You can still succeed and there are cases of people who took only the SN and have been successful.
Simply without AE, the probability of success is decreasing. I can't say how much.
If you do not vomit for the first few minutes, you will most likely die (if you have taken care of all other things).
I do not consider AE necessary, but if someone wants to maximize their chances of death, they must get them
Of course, CTB is a drastic decision, so logic suggests to take care of everything and leave as little as possible for failure.
To sum up: you can CTB without AE, but you reduce the probability of success. It's hard to say how much, because it depends on other factors.
But probably even without AE the chance of success is relatively high (don't take my words completely seriously).
You must answer the question yourself whether you want to increase the risk.