Yes, mine (for external e-mails) typically says somethingalong the lines of “I’m out of the office until [date/time] and messages to this address are not monitored in my absence. I will respond as soon as possible on my return. If your message is urgent, please re-send to my assistant [email address] or telephone [assistant’s number]” Internal it will usually just say “I’m out until [date/time] pass any urgent enquiries to [co-workers] ” although my assistant and a couple of others have my home number and personal e-mail so can get hold of me in a genuine emergency, and I will sometimes speak to them in advance if I’m willing to lower the bar on what amounts to an emergency, but I would not expect any of my employees to do that !
But this absence of basic travel cybersecurity is a problem. Email is the number one threat vector for socially engineered attacks. An automatic reply message not only sends the information to designated contacts, but it also bounces back to people who send phishing emails. Threat actors use any details found in OOO messages to craft targeted social engineering messages. Well-targeted messages build trust that threat actors take advantage of.

Thank you for getting in touch! I’ll be out-of-office from [date] to [date] and will not be checking email during that time.
My office has a shared vacation calendar, which I think is a more helpful way to handle this.