I actually experimented a while ago by running a long-running Twisted-based daemon on top of PyPy to see if I could squeeze more speed out. PyPy did indeed vastly increase the speed versus the plain Python version, but once I discovered that Twisted was using select/poll by default and switched it to epoll, my performance issues with the original CPython version were gone (and PyPy couldn't use Twisted's epoll at the time).
Another major issue was that running the daemon under PyPy used about 5 times the memory that the CPython version did. This was a really old version of PyPy, though, so they have probably fixed some of this memory greediness.