Do what I do: Buy 2 pairs. One for clay, one for hardcourts.
While the tread on the clay shoes will be OK for hardcourts after the clay season is over, the cushioning will likely be shot. And if you are like me (older, slightly overweight), the pounding your ankles, knees & hips take on hardcourts will add up over time. Its worth the extra $.
Now, the ultimate question: Do you need clay-specific shoes? Well, that depends on whether you adjust for clay (e.g. slide into your shots) or continue to play hard court tennis on clay. If the former, then clay specific shoes will help. If the latter, then don't bother.