Once a user has allowed for a getUserMedia request to access their camera/microphone, is it possible to programmatically "remember" that permission across future page loads?
Not sure this answers your question, but for Chrome at least, if you use HTTPS, permission is only requested once. (Looks like this isn't implemented in Firefox.)
For Chrome apps you can add audioCapture and videoCapture permissions, which mean the user is only asked for permission on installation.