Well yeah you could do that, depending on how you define "load the page". For example if you have a main content area of your page that uses ajax to load the contents of it (a separate request from the initial page request), you can throw up a preloader while its doing that. IOW,the "preloader" things you see are basically achieved from loading new content (with ajax) on a page that has already been loaded. You basically separate the page load into separate stages: first a basic "container" with the preload stuff, where you can show the preload message, and then the "content" stuff that loads separately (with ajax).
So when you say that there is a preloader before "going to the next page", one of two things is happening:
1) You aren't really leaving the page. You stay on the same page and some container on the page is being loaded with new content (with ajax), and the preloader message is displayed until that ajax call is complete. This is what most sites do, what you normally see. And this is fine, especially if it takes more than a second or two to load the new contents up.
2) If it really does take you to a whole new page..well that preloader isn't really preloading the next page, it's just showing you a message and redirecting you to another page eventually. That message you are seeing is pointless and just making you unnecessarily wait before the redirect, as far as actually loading the next page.
I rarely ever actually see people doing scenario #2 for the hell of it, however, I do see this happen on sites sometimes. Why? Usually a site will do this when they want to do "cleanup and save" type operations before letting you proceed to the next page. For example, a website may be tracking clicks on a page, so they might execute the tracking script (such as Google Analytics). Or perhaps they want to make an ajax call or two to save some stuff on the page into some server-side session vars. So they want to make sure operations like these are complete before redirecting you, but they don't want the visitor to sit there seeing this delay before redirect, so they throw up a "loading" message as a distraction, because it sounds better to tell a user "please wait while the next page loads" instead of "please wait for this current page to finish doing 'unload' stuff".