3G Watchdog uses little battery, typically under 2%. To verify this, look at phone Settings > About phone > battery usage. You will see that most of the battery is used by the Android OS and the display, and most of the time 3G Watchdog is not even listed.
Note that while the phone is sleeping 3GW may wake it up periodically (without turning the screen on) for less than 1 second in order to check that the 3GW service is still running in the background and counting your usage. This has no significant impact on your battery life.
See also the question “Can I have a longer (one day) update period?“.