Hi, Annette. Welcome to ATP!
I've heard that willow bark tea is useful for root stimulation, but I think that the benefits are largely due to the use of recently living plant materials.
I wouldn't imagine that processed or synthesized aspirin would help any more than applying some good compost around the plant or feeding with seaweed or fish emulsion. Both of these seem much more likely to have what an ailing plant needs, and probably in a much more readily available form.
Do you have an ailing plant now? If so, is it a recent transplant or is it an established plant?