That's pretty much the idea, with a few extra add-ons like console logs and plugging into existing customer support channels.
I've found this type of feedback tool to be really helpful in reducing the amount of back and forward when handling suggestions or problems in web apps. Hopefully it'll, at the very least, make the "What browser are you using" reply go away.
Nice widget, congrats on launching! I'd love to see it in action without signing up though, so you might want to consider adding a giant "demo" button somewhere.
[0] https://www.google.com/tools/feedback/intl/en/images/preview...