Yes, it’s an FTP client and one of the best there is, in my opinion, but it’s also 100% capable of functioning as a local file browser and management tool. Like most FTP clients it has the typical split-pane interface that everyone’s familiar with, both of which can be a local browser.
Now, I’m not trying to pull the wool over anyone’s eyes by crowing about Mac being so good at everything, etc – obviously any decent FTP client for Windows (FileZilla, CuteFTP, WS-FTP, SmartFTP) will be able to do the exact same thing. If you’re a Windows user this article is a tip for you, too – it’s much easier than using multiple Finder (OS X) or Explorer (Windows) windows.
In Transmit it’s simply a case of clicking the "Switch to local browser" on the far right of the main Transmit window, as shown below – it’s the round button to the right of the word "WebDAV".