Is it possible for my mobile carrier to track my wifi usage and bill me accordingly?
Of course not. Your WiFi will go through your WiFi chip to AP and to some other ISP. There is no connection with 3G just like you can use WiFi even without SIM.

But your carrier can(though highly unlikely) use some tracking program to track you and find what you are doing. Even if they do, the WiFi usage won't be counted as 3G.

One advice I'd like to give you is sometimes you think you're on WiFi but due to many reasons you might not be connected to WiFi and you might be browsing over 3G. So just keep an eye for that.