No, it doesn’t and can’t set $URL as Tinderbox lacks AppleScript support for such an action. Let’s say you’re at www.example.com/somepage.htm and you select 2 sentences “This is one. This is the second”. When you use the clipping and Tinderbox’s focus is - as intended - in the view (left) pane the result is:
This is one.
This is one. This is the second.
If you’ve put put the focus somewhere else, e.g. the $Text pane you will get an unexpected result.
I’m not a programmer and the service file is not supported software, just something I tried out as a fellow Tinderbox user. If it doesn’t work as desired, you can use Automator to edit it and alter the code to make a new version that suits your needs. I’m no expert in services so likely you’ll have more success than me.