Thanks @wlongo,
You might check out the Bots section in Community Applications, as you can use these to add a bot account to a private channel and get close to what you want I think.
Please let us know what you think (and if you try it, what the results might be?)
In my mind, it's higher priority to add more bot support than to put outgoing webhooks into private channels. You can see when there's a bot in your channel listening, it's harder to tell when there is an outgoing webhook listening.