that sounds okay, beets are good for you, and the homemade juice sounds really healthy. i'd say if you literally ate nothing but beets it would be bad, just because you weren't getting any protein of carbohydrates or anything, but as long as he sticks to a balanced diet, he should be able to drink as much beet juice as he wants without anything bad happening.
Also, beets have vitamin C, which in huge quantities can give you a headache, but you shouldn't have to worry about that to much.