Work, yes, fit, maybe not. Some of the larger application pumps mount a bit different and are larger in diameter. When you go to put the sender assembly back in you'll find that it won't fit.
When I installed the Buick SC pump, I had to trim the float arm pivot point to get it in. Very tight.
Frankly, I'd be surprised if the LS1 pump didn't need the same thing.
Also, the flange on the bottom wouldn't fit so I changes the way it was clamped. The result was that it caused an annoying whine in the passenger compartment. I had to pull it back out and change the way I mounted it.
So if someone says it will fit, make sure it will fit right.