I wouldn't bother explaining via email to the whole group.
And speaking as a celiac sprue person, let me share my perspective on "keeping quiet": I am so incredibly grateful to all the people who have walked this path before me.
Because of them, almost every single restaurant I've gone into here in NYC has had a gluten-free option--even if it's not on the menu, the servers are aware and alert, and I feel I'm getting credible info. (And though I never have discernible symptoms to tip me off to accidental exposure, my last test was clean, so...)
Therefore, I'm a bit of an evangelist. I figure, if the non-celiac people around me hear about my diagnosis, they'll be that much more alert to the needs of the -next- celiac person they encounter. And they'll be more likely to be the ones who say, "Oh, rats, let's find a different restaurant."
So while I don't think you need to run around blabbing your medical info all over the office, I think especially now, you can say, to anyone around you, or so the few officemates who might actually care that you aren't staying, "I can't stay, because the restaurant has zero gluten-free options, and they aren't even willing to work with me. It's not just a fad diet, I have celiac and I'll get really sick if I eat it, so since I'm basically sitting here watching you eat, I'm going to peel out. It's been fun working with you. Bye!"