Abhi can a website work without it ?
Sure, what is stopping you ?
While Google Analytics can give you a lot of information about your visitors and perhaps the most dependable source for the actual no of visitors, there is no compulsion that you should use it. Bot traffic is effectively filtered by Google. And you get a break down of your visitors' OS, browser, location etc. If you not a person who likes planning with the help of these stats and want to make sure that no third party code is used, by all means, skip it.