"Yes" and "I don't know"
"Yes" I think so if difficulty adjusted every block, and "I don't know" (nor do I want to know) anything about LCC
From previous edit not sure you saw...
Edit:....So it clicked in my head on my hangup. If rest of world shut off, then we would never throw work away. Every block we try to crack and dont crack, that is wasted hashpower. So if we have no competition, every hash and all the work we send to the block will result in a block. Right now we only have a very small percentage of actual work that results in a block. How could that not speed up block generation over expected?
There's no "almost there"
Using the dice example again (since yes it really is the same as bitcoin hashing):
If you roll a dice ten times and miss getting a "5 or a 6" you are no closer to getting a "5 or a 6".
It doesn't matter if you rolled and failed ten times, or a hundred times, the previous rolls don't affect the next roll, and don't affect your chances of the next roll getting "a 5 or a 6".