Detect if webplayer is supported or not from UserAgent

Is it possible to detect if the unity webplayer plugin is supported or not on the server-side before serving a web page request?

We're currently building a Facebook application using Unity3d. We would like to track the success-rate of the sign-up process for new users, and ideally we would filter out users who can't install the unity plugin. To track the sign-up funnel, we send the first metrics event from our server. Is is possible to detect from a User Agent if the unity plugin is supported by that browser/OS?