You will at least have to handle the events for the window, or you will be unable to move or close it.
Other than that, you can do completely without events, but it is a really, really, really bad idea. User uses a different keyboard (different, as in language) and you're screwed. User clicks very fast, and you miss the click. User does <insert one of 1000 other things> and you're screwed.
Events work, and they work well. Plus, they work with different languages, with different devices, mappings, resolutions, different anything. And they don't burn CPU time polling.
One good example where polling keyboard state results in a total fuckup is when e.g. US American programmers assume that "/" is a proper key and uses it for some interactive control, and your end user has a German keyboard. With events, it is a nuisance since you must hold down shift before pressing the key (holding it works, at least), but if the program samples the keyboard state, the program is totally unusable (there simply isn't a way to press any combination of keys that works). Similar for []{}\.