No, you cannot use a fake address when creating your Amazon seller account. As of 2021, Amazon has begun mailing third-party sellers postcards in order to verify the business address.
Another layer to why you cannot use a fake address is that in September 2020, Amazon announced that they would be requiring all U.S. sellers to disclose their business name and address on their public profile. The reason for this change was pretty straightforward: they wanted to help buyers better vet third-party merchants who may be selling counterfeit or unsafe products.
So, how can you solve this issue of getting a real business address and protect your privacy to open and maintain your Amazon seller account?
For more details you can check out this process here.
You can also check out these other resources to help obtain proof of address to open your Amazon Store.