Unfortunately, no. That is something you would have to track internally in your application. Most likely using a flag that you set before calling the Close method.
There are some edge cases were we cannot really determine if it was a user-initiated action. For example, if a tool window is in a floating window and the floating window is closed (via Alt+F4, system menu, or programmatically), then we are only notified that the window is closing (and thus the tool window must be closed as well).