I've driven a Boxster 987S with the Sport Chrono option which was a manual transmission. I noticed a difference in throttle response. Remember that the response will increase more as you go faster (in mph). The brochure depicts this on a graph in more detail. If you can test drive one first, you can answer the question for yourself more confidently. When I order mine, I'll be requesting Sport Chrono along with PASM.
For less than $1000 US, it's a no brainer for me. If you are a techno junkie like me, and can afford the option, you'll probably enjoy the feature along with the timer.