In testing I've found that there is a split between people that use the browser back button regularly, and those that never use it.
Also, remember that the browser back button takes you back in history, not back in navigation, and so isn't appropriate for navigation purposes. E.g. If someone enters a page via a shared link or bookmark, they won't have valid navigation history to go back to. back.
If you rely on the browser back button, you are looking for problems. You should make sure that your website is navigable with only what you provide within the website.
TL;DR: Don't rely on a browser's back button for site navigation.
Edit: To be clear, I'm not suggesting that you should use a back button. In fact in most cases, it's simply an excuse for a poorly thought out site structure.