Yes, it is possible to have both Commercial and Trial version running on the same machine provided they are installed in separate directories or folders.
NOTE:
1) You will still need to run the install both Trial and Commercial versions.
2) During the install of Toad 'Trial', ensure that the installation destination folder shows 'C:\Program Files\Quest Software\Toad for Oracle TRIAL\' so that the two versions will not overwrite each other. It should default to that already, but still please just verify.
3) You should also end up with two Desktop Shortcuts. One should say 'Trial' ion the shortcut name.