I'm not sure I understand your question. Running an application using POE (or indeed any other perl module) shouldn't affect the accuracy of your PC's clock. That depends largely on the hardware in the computer (which is generally pretty inaccurate from what I remember).
If your problem is that you want this application to generate logs with an accurate timestamp, then the ONLY way to do this is to have the PC's clock synchronised with a remote source that is more accurate. NTP is ONE way to do this. You could, of course, invent your own alternative to NTP (Microsoft did this with their "domain time service") - however you're unlikely to get anywhere near the accuracy of NTP by rolling your own (as Microsoft demonstrated).