I don't disagree, but when I've tried this I just find myself doubly exhausted: once (mentally) from the work, and again (physically) from the gym. Still agree that making time for the gym is really important though. But for me, it's not the answer to mental exhaustion but rather just part of a healthy lifestyle generally (personally, proper sleep hygiene is the only solution I've found to mental exhaustion and overwork).
When you walk into the gym you need to stop thinking about work and start focusing on your workout. For me, this comes in the form of planning which exercises I'll be doing, how much weight I lifted the previous time for how many reps, and how much I can increment it. And then during the lifts, I focus on the mind-muscle connection to make sure my form is correct and I'm activating the right muscles.
Trust me, when you do it like this, it's incredibly relaxing from a mental perspective. I actually look at my gym sessions as meditation time.
It took me a few years of consistent intense training to really get into the groove of things. I've been at it for about 9 years now. This is the intensity that I aim for (mind you, this is not me in the video): http://www.youtube.com/watch?v=LAhNyvTF5Uw
After that level of intensity on a consistent basis for a few years, you adapt to it. While you may feel tired, you gain energy from it as well.