However, I do not know if I need to install the WinSCP.exe on the application server and have it running in the background all the time for it too work.
Yes, you will have to. There's no API in FTP/SFTP to get notified about the changes. You have to proactively poll the server for changes. See https://stackoverflow.com/q/1277239/850848
Here is a PowerShell example of such code: