Is backup mandatory for upgrade to iOS 6 in iPhone 4S?
If everythings runs smoothly (as is usually the case) you won't lose anything, nothing will get deleted.

But even the best engineered update process can fail. So it is best practice to back up an iPhone on a regular basis and specially before updating (like with any other device/computer, for that matter). Why? Because sometimes things go wrong. And a backup is like an insurance policy on your data.

Luckily Apple makes it easy: iTunes always backs up your iPhone before updating. If you prefer an over-the-air update, you can back up you iPhone to iCloud.

(I prefer backing up to iCloud, a friend of mine overwrote the iTunes backup after a failed update and lost all data.)