No. It will not effect your jailbreak in any way shape or form. Only updating the iOS on your iPhone directly will unjailbreak Your device. iTunes has no effect on the jailbreak. Don't worry.
Feel free to update to iTunes 10.5.3
That's ridiculously a wrong information. Factory restoring or Updating the iOS using iTunes will format the device and load into the device a brand new iOS. The only thing which will not affect the jailbreak is syncing the device to iTunes. Syncing musics, apps, contacts, etc. Once hit restore or upgrade, you can say bye bye to your jailbreak. And that's why you should restore or upgrade your jailbreak iPhone using iTunes before taking the iPhone to apple in case it develop a problem.