If your installer is a native application, theoretically, yes. Because Firefox is a native application, you could reverse-engineer, and/or study Firefox’ open source code, and spoof whatever Firefox does when the user approves an extension. In addition to copying your files into the profile folder, you will probably need to add objects to the prefs.js file. But there may be more to it than that. And whatever you do would be completely unsupported and subject to breakage in any new Firefox version. Finally, your installer would probably need to first quit Firefox if it is running, before so messing with its files. So if your purpose is to make the installation seamless and unnoticed by the user, you’ll be wasting a lot of development time.
Unless your purpose is a hacking challenge, I recommend instead doing it above board, as I described in my original reply