I would try it. Most plants are highly adaptable, and roots will generally crawl around anything in their way. (Otherwise, they'd never make it past the first rock encountered underground.)
If there's any worry about competing roots, I would opt for shrubs or some other rugged, spreading plant over flowers. Would you consider star jasmine? In my own experience, the most indomitable root system I have ever encountered belonged to a row of star jasmine next to my mother's house. One might think these delicate little flowers would have an equally delicate little root system, but I can attest that the roots on my mom's jasmine actually knocked bricks aside throughout their slow but steady growth, (Star jasmine also smells wonderful, and attracts bees to the rest of the garden.)
The only thing I would be concerned about is whether the tree root is dead or alive. Alive, and you might find it sending out new sprouts. I've had this happen with everything from oak stumps to eucalyptus stumps. Although it might be a nice surprise to encounter spontaneous life, a stump (or root) with enough life in it may very well choke out the roots of the plants you're trying to grow over the top of it.
If the stump or root is dead, all the better, as it should eventually rot into the ground, making for some lovely, natural compost. The only thing I would worry about with a dead stump is the reason it's dead in the first place. If somebody cut down a tree, that's one thing, but if the tree died from disease, I'd make sure the disease wasn't one that could kill your new plants as well.
