Cooling the wort with frozen wort

I use an all grain setup with an immersion chiller. In the summer time it still is pretty long to cool my wort down to pitching temps. Has anyone ever tried freezing pre-made wort and throwing it in their BK when cooling? Same idea as throwing in ice for extract brews, but it wouldn't water down the finished product. I'd just make some wort the night before my brew when I'm cooking up my yeast starter.

Things I would consider:
Targeting the same OG for the frozen wort as I would for my brew.
Sanitizing everything of course.
Not using too much, probably around a liter frozen into a plastic container (maybe use a big chinese soup container). I figure this will be a pretty big block of ice but not too much volume
Should I have concern if I'm not boiling my pre-made frozen wort for the full 60 minutes?

One litre of frozen wort will not have much cooling capacity. Better to freeze water, and put your kettle into a bath w/ ice IMHO.