That’s exactly how I set up mine, except that ordinarily I’d have several options, like: “If you need help with X, call A. For help with Y, call B. For help with Z, call C. For anything else, call my manager at extension 000.
As a “don’t try this at home” anecdote, last week we had an all staff retreat, and we were asked to put up away messages. I put a perfectly professional one up for outside email, but in a fit of whimsy, the internal mail triggered an away message that said “Why are you emailing? We are supposed to be paying attention to the retreat!” I figured, we were all at the retreat, so nobody would ever know. Of course, someone did email me 30 minutes before everything started, and triggered the message. Fortunately, he figured out it was an away message and thought it was funny.

I don’t include this much detail on my OOO, but I do include if I am out of the office for religious observance, because I don’t use electronics on my holidays and want people to know that I really won’t get their message until the holiday is over. (Unlike the norm in my workplace that otherwise senior people are checking email even if we’re sick or on vacation. I know, I know.)
If I am out of office for more than one day, I will update my email out of office message “I am out of the office with limited access to email until {X date}. Please direct any questions to {support department email}.”