I got very skinny when I first turned vegan. That was essentially because prior to that point the only fat in my diet was cheese, and for the first year of being vegan I ate the same diet just without the cheese. It wasn't balanced and I didn't plan it particularly well. I wouldn't describe it as a health benefit.
After a year, I had two very bad colds where I was bed-ridden for a couple of days each time. I fully knew that having a bad cold could just have been down to bad luck and may have had nothing to do with diet, but still, I did take the opportunity to re-examine my diet and resolved to make more of a concerted effort with the fatty acids.
I am some 2 stone heavier than that now, and have not really suffered much from colds in a few years - but those two facts could still be just coincidence. I don't think there's any clear evidence to connect them. Sometimes you just get ill because some idiot sneezes the hell over everything.
Generally, during the last 11 years of veganism, a previous 4-5 years of on/off failatarianism, and prior to that a childhood of staunch devotion to the Temple of the Golden Arches, I've gone through periods of eating well and periods of eating badly, of salad binges, chips binges and cake binges. In that time I haven't knowingly been deficient in any nutrients or had any allergies or dramatic weight swings. In my personal experience, the highs and lows of my day-to-day health and well-being seem to have correlated more to sleep, stress and exercise factors than they have to diet.