Generally, yes, since most applications are installed through copying the application from a DMG file into your Applications folder. However, this is not always the case, since applications can also be installed through the use of OS X Installer or a 3rd party installer.
As a rule of thumb, if an application was installed through an installer, copying the.app from the Applications folder won't be enough.
If you wish to backup an application that came justbackup 1.5.6 with serial key from an installer, you will usually require that installer. If you have a valid license for the software (e.g. Photoshop) you can redownload the installer from Adobe's website and use that to install it.
When you entered your key into the application, it will have created a hardware-linked key that ensures the software cannot be copied to a new computer without re-entering the software key. The easiest way is just to use the installer itself to reinstall the software.
In addition, don't forget about the additional files that may be created when you run the application. For example, files in the Application Support folder. You can use an complete app remover such as AppCleaner to list the files that may be related to the app.
In this case, there was a.plist preference file in /Library/Preferences that holds DaisyDisk's user preferences. Copying this file to a different computer in the same place should keep the preferences.
On the other hand, cache files such as those in /Caches are not usually necessary to be backed-up/copied.