Very little - the proxy seems to add fractional seconds per message (see the logs while it's running) but it might "feel" slower in your mail client due to the batched-then-dumped nature of things. The proxy buffers up the whole message, then the client gets it all at once, rather than trickling in. You might see jumpy progress bars as a result sometimes.
One of the biggest lag problems with a SpamAssassin scan happens when SA spins off into the weeds on truly large messages. This may be an acceptable delay in a store-and-forward chain, but in a real time network proxy it's fatal. Pop3Proxy works around that (like many SA apps) by declining to scan messages over a certain size - 250K by default, but it's configurable.
See the discussion on the manpage for more on that.