Basically, it might technically be "edible" but you might not enjoy it and there is does not hold the same nutritional value as it does the first year.

"...Most field guides focus on the flowers and will not show you the first-year plantÂs striking leaves, which can be as long as your arm and half that width, with wavy edges and whitish fur on the underside. The first-year leaves are known as "basal" leaves, since they form a "base" of leaves, growing straight out of the ground, not on branching stems. Yet this rosette of basal leaves is the form you would seek if you wanted to dig a burdock root for eating. An understanding of the biennial life cycle will show you why.

The second-year biennial, with all its energy invested in producing flowers and seed, its last act before death, has no nutrients left in its root. If you dug the root of a burdock that was flowering or going to seed, you would find a tough, fibrous, inedible substance. The sweetish, white-fleshed root of a first-year burdock is what you are looking for. However, even in the first year, there are better times than others to harvest.

In the first summer of its life, as the young plant is growing, the minerals and water gleaned from the soil by the roots are being sent up to the leaves so they can put on bulk and manufacture more glucose through photosynthesis. Glucose is heading down to the roots to combine with some of the minerals and increase the size of the root. The regular exchange of nutrients makes for a decent-tasting root. But after a good hard frost, the leaves begin to die back, and any nutrients produced or taken in by the plant are stored in the root. Fall is the time when the roots are sweetest and packed with the most vitamins and minerals."

http://plant-species.suite101.com/article.cfm/wild_edibles_and_life_cycle

"Grow and Harvest Burdock
Native to Europe and Asia, burdock now grows like a weed in temperate areas of the United States. Look for its distinctive spiny, burr-like heads. Burdock is a biennial plant  the best time to harvest the root is during the fall of the first year, when the plant has large leaves that are green on top and grayish underneath, or during the spring of the second year. During burdockÂs second year, the plant has purple flowers from summer to early fall."

http://www.herbcompanion.com/herb-profiles/Burdock-Does-It-All.aspx

Thank you Violet