Android 2.3: Expected behavior for setting time automatically with Wifi only
Android only supports Network Time Protocol (NTP) from Android 4.0 on and before it was NITZ/GSM only - certainly not in my opinion.  The app ClockSync which I use in my LG Optimus One (P500) running Android 2.3.3 (rooted) works with NTP protocol. I did not rely on my GSM operator's time settings as I found the deviation was unacceptable limits.

Please see the question Inaccurate time? How to fix it? and its answer.