Many of us in my department do this all the time, but we all also receive a ton of e-mails so it helps to get a heads-up that there's a timely e-mail that has been sent. I often ask people who call me about something to send me an e-mail about it because, otherwise, that means I have to write it all down as a reminder (also, when it's one of the staff with a request, it's so I have it in writing from the person). I don't think I've ever had a problem with getting both voice mail and e-mail on the same thing when it's work-related. I don't think anyone else in my department has either. I guess we're fortunate that seems to be a normal work practice for us and that no one gets bothered by it. However, I do work in a hospital, and my department deals directly with things affecting patient care so a lot of our communication IS timely. I also work on the inpatient side so many of management in my section are often busy running around the hospital and would appreciate the verbal heads-up that an important e-mail has been sent to them, rather than finding out only once they have a chance to check their e-mail.
Now, on a personal note, I do have a problem when DH calls and e-mails me at work for something that isn't urgent. He did this to me just the other day after a big project was sent to me (hours of work). He calls my work phone to tell me he has decided to do X thing; I was a bit aghast and replied, "Can we talk about this when I see you at home tonight?" (he was calling to just say something like "I decided to go ahead and buy tires next week"). I then looked at my e-mail after I got off the phone with him and discovered he had just e-mailed me about the same thing a few minutes before he called. I had a discussion with him about contacting me about something non-essential and non-urgent in the middle of my workday when he had also just e-mailed me. DH knows I'm under an extreme amount of stress at work right now and am now so bogged down by work I've fallen 1-2 months behind on timely tasks. I warned him this was coming 4-5 months ago and again when it started three months ago so why he felt the need to contact me via e-mail AND a phone call (e-mail is fine because I can read it when I have time) is beyond me (I asked him about it later, and he said he thought it was something I needed to know right away...I don't agree and still don't get it -- I did have a good laugh over the incredulity of it though).