It all depends on how your body responds and what you're eating.
I've gotten excessively fat on a vegan diet in the past by eating whatever I wanted and because I didn't pay attention to food quality or calories taken in, so there's really no single diet where you CAN'T have things go that route if you aren't careful.
But, if you're eating whole foods with tons of good vegetables and minimal processed foods, there's a lot less chance of putting on excess fat on a vegan diet. Being as there are still a thousand vegan junk foods out there, not to mention the quick high calorie foods like rice, pasta, etc. it's definitely possible to get plenty of fat on you if you eat the wrong things and too much of them.
I've been vegan for about 13 years and have been counting calories for the greater part of 18 years now, and probably will continue to do so for a long time. I need to keep things in check, otherwise, they get out of hand quickly. I don't keep a log, rather, after all these years I just have become adept at being able to know the calories of what I eat within about 5% margin of error, and it's easy enough to keep a running tab in my head, so you may not need to be overly meticulous, but it doesn't hurt to keep track of things for a while just to make sure you keep going in the direction you're hoping for.
"A 'hardgainer' is merely someone who hasn't bothered to try enough different training methods to learn what is actually right for their own damned body." - anonymous