To clarify, AppBrain is just an indexer of the Android Market. It does not "have" apps. It just points your phone to the files on Google's Market servers. The Fast Web Installer will only do OTA installs with free apps, because the pay system for apps is tied to the actual Market app.
If just using the AppBrain app (i.e not the Fast Installer), it just links you to pages in the Android market app. AppBrain is a good service to use, but it's hindered by the fact that is is a third-party set up. The site is well designed and helps surface good apps, though.