It is unlikely. Although procmon does monitor everything the application does, you actually have to perform all actions in order to fully get the entire scope for that application. Not performing a certain task may not expose a certain registry key or file that you miss.
Then again, procmon does not tell you which dll's it registers. One dll may actually load another dll and if you filter solely on the application, that action is not shown.
You would want to start with installing that application to the other computer, then copy the entire folder over, and by monitoring you may see some additional settings which is a much better approach, but even still you may not have everything. But given that it includes an install, it does not conform with your question: move the program.
But if you want to move programs from computer to computer, the easiest way is to start using portable versions of programs or find alternatives that have a portable version. They don't write necessary files to the registry and keep all files in the same folder (or subfolder of) of the program. There are even sites dedicated to portable apps, such as www.portablefreeware.com