I have wondered this myself. It must be possible as the manual for TH3 does make a couple of references to "standalone mode". The manual you get with TH3 Cakewalk edition appears to be the same one you get with the full version of TH3.
My guess is the standalone mode is only available with the full version. If you have the full version, the installation may have populated the start menu with the required shortcuts that points to the standalone mode. If you have the full version of TH3, then I would hunt the start menu for the required shortcuts. You may also want to do a full file search for something like TH3*.exe. Maybe it would be under c:\program files\...
As I only have TH3 Cakewalk edition, it looks like I do not have the executable for the standalone mode. I can't find any shortcuts, nor can I find an exe file on my system for TH3 standalone.