Can a python script on my server access the webcam and audio input of a user as easily and as well as a Flash plugin can?
Server-side web scripts have no access to the client other than through requests. You need to use JavaScript, Java, or Flash to access devices that the browser (and consequently user) allows them to.
No: the "plugin" you mention runs in the user's browser, your server-side script (Python or otherwise) runs on the server, a completely different proposition. This relates to your other recent question about a server-side script accessing information on your desktop: your client machine tends to be very protected against possibly malicious server-side apps (never enough, but everybody keeps trying to make it more and more protected these days).
Not as easy, no. But there are extensions you can use. E.g.
A Win32 Python Extension for Accessing Video Devices (e.g. a USB WebCam, a TV-Card, ...)
http://videocapture.sourceforge.net/
Tutorial: