It really depends on which intake you have...some are set up for either a spread bore or Holley/Edelbrock(square bore).
Chances are, tho, you'll need an adapter. Then, you're gonna have hood clearance issues.
You can use a Holley carb with the original air cleaner base, depending on which carb you get, or want to use. The stock base won't work with a double pumper carb, but...they did use some pretty large Holley carbs on the LT-1 engines, so you may be able to find a base for one of those, and be okay.

SO..is there a problem with your current carb?

I had the original holley carb with an aftermarket intake on mine when i purchased it, which also meant i had no choke.  i could have put stock intake back on with holley and had a choke or change carbs, which i did went with elderbrock (kept the holley)  really seems to work good, you might have to go with an lt-1 style hood for the cleareance but i am not an expert like the other gurus on this sight.
BTW, could you give me some feedback on that laguna grey color, i know it was not a color that was used alot, about 5 or 6 per cent if i remember correctly, and that was the original color of my LT-1 and been thinking about repainting back to stock color, wife says no way, some imput on the color from an owner would be nice, great looking vette.
Larry

JC,

The LT1 air cleaner REALLY drops low over the carb.  We sell quite a few to people with a slightly taller intake and stock hood.  And they are pretty!

Larry