This is an acceptable ask in the companies I've worked in the U.S., especially for a small business. My experience is that people will email you much less than you expect, and it's just for emergencies
I don't think the problem is how many emails you will receive. It's how often you will be expected to check your email and how quickly you will be expected to respond.
I mean, if I an on vacation in Hawaii, what if I want to go on an all-day snorkel trip? I probably won't be able to check my phone a lot, and I certainly can't do anything if there is a real problem.
