A healthy lifestyle, including a healthy, balance diet, will definitely help keep your skin healthy. Staying hydrated and exercising regularly also help keep your skin healthy. A healthy body is more likely to have healthy skin. Of course, diet isn't the only impact on your skin. Environment, hormone levels, genetics, all these things play a role in acne. Diet is usually the easiest of these things to change.
In my personal experience, my skin got exponentially clearer when I cut dairy out of my diet. I have a family history of lactose intolerance, and I noticed that I tended to break out worse when I ate more dairy than usual. So I cut it out almost completely, and now I rarely get any blemishes. I don't have very good willpower, and will occasionally cave in and eat some cheese or a little bit of ice cream, and usually have a break out of cystic acne in the next few hours.
So I really do believe that dairy causes my skin to break out. However, that doesn't mean that ALL dairy causes EVERYONE to break out. If Whole30 helps you get on a healthier track, then by all means, try it. But try to remember that eliminating all those foods isn't a miracle cure for your acne. I found that just paying attention to what I ate and the way my skin reacted to different types of food was more successful than any diet plan or skin care regimen.