It does carry over to L3/L2/L1 cache, but only if the tree is designed to benefit from that. See http://blogs.msdn.com/b/devdev/archive/2007/06/12/cache-obli... for one strategy to do that. (With that structure lookups become faster, but walking the tree in order becomes difficult.)
This is a really great article and I wish I could give you some more points to make this appear higher. I once used a cache-oblivious matrix transpose algorithm that was startlingly simple and effective but I didn't know the approach had been so widely applied. Thanks!