I used to work with someone who had a message telling people she only checked her email twice a day. You pretty much needed to call her if you needed anything outside of those times. (She worked in a remote office.) I think she had read one of those books on efficiency that recommended scheduled email time. But there were problems with this: 4. My department often had to email attachments or text to illustrate our questions/concerns. And we were on deadlines. Reading a page of text over the phone was not an efficient use of anyone’s time 5. She did outreach & was often out of the office on site visits, trainings, or travel to these places, but never ever set her OOO for these, because she was “working.” However, she was effectively not available to read emails from other staff until after hours on those days.
When one of my colleagues is out of the office, he doesn’t mess around. In fact, he’s turned his auto-responses into a running series of commentary from fictional cartoon character Troy McClure.

She continues: “However, there should be a way for whoever is emailing you to have an urgent request handled, and that should be included as part of your OOO as well as being known to your work team (supervisor and colleagues). That might look like including a coworker's email on your OOO or it might simply involve setting a forwarding rule for while you're away, so that your email goes to the colleague who's covering.”
Thanks for getting in touch. I am currently out of the office from [date] to [date] and will have limited access to my email during this time. You may be able to get ahold of me on my cell phone at [phone number]. If you can’t get through to me and have an urgent inquiry, you can contact a member of the team at [phone number], or my assistant [Name] at [email] or [phone number].