There's a video on YouTube called "Sugar: The Bitter Truth", a lecture by Robert H. Lustig, MD, UCSF Professor of Pediatrics in the Division of Endocrinology, that (from my understanding) implies that, at least in the context of taking in copious amounts of unhealthy sugars such as sucrose, fructose, and high fructose corn syrup, you can offset the bad effects of those sugars by burning them off as quickly as they are processed in the liver. It would definitely take a lot of work to do that though.
However, there are a few problems with the theory of just simply eating junk food. Junk food rarely contains enough useful vitamins, nutrients, and electrolytes to maintain healthy body function, without having to rebuild muscle tissue that is damaged during a workout. Additionally, according to About.com and several other sources, excessive exercise increases your risk of injury.
Most junk food contains high fructose corn syrup, which inhibits the body's fullness mechanism, causing you to eat more than you actually need. This will cause you to need to exercise even more to burn off the excess. It goes without saying that you need proper electrolyte levels. You also need protein, and protein causes you to need calcium, etc., etc. In order for your body to properly process one nutrient, you typically need an appropriate level of two others.
Sodium, potassium, calcium, and magnesium, along with bicarbonate (which your body builds from water you drink and the air you breathe) are important electrolytes. While you're likely going to get plenty of sodium from junk food (probably enough to cause water retention problems), you are unlikely to get much potassium and magnesium, and you aren't likely to be drinking much water.
So, since maintaining an unhealthy diet of junk food will prevent you from taking in the vitamins and nutrients needed to restore damaged tissue, and excessive exercise is a known factor leading to an increase in injury, you're likely to spend more time recovering from extreme muscle soreness or serious injuries than you are going to spend exercising, and thus you won't be burning off the excess unhealthy sugars in your junk food diet.
In the end, you're going to be dealing with a host of short- and long-term health problems by eating unhealthy and thinking you can work it off.