There have been a few GT40 replicas built with Chevy engines. Also, Wayne Presley posted a photo of one with a Maserati engine (later it dawned on me that most likely the Maserati V8 came with a 5DS25 ZF attached to it, so it was more logical than it looked at first).
Well, I suppose you can put any engine you want in your car. And before everyone gets bent out of shape, we're only talking motor vehicles here, not life or death decisions...still, you should consider the following:
-these cars came into existence by the efforts of Ford and the designers and engineers who worked with Ford. Modern GT40 replicas are tributes both to the beauty and functionality of the original design, as well as honoring the efforts and dedication of the Ford teams working under the Total Performance banner. Installing a Chevrolet engine seems odd and wrong to me, almost disrespectful of what the car stands for.
-resale of a GT40 replica is somewhat difficult. The market is limited, and the owner usually loses money. Resale of a GT40 replica with a Chevy engine would be that much harder- you would probably have to pull the engine out and put in a Ford just to sell the car, and sell your Chevy engine separately. Lots of trouble, and more expense.
-essentially power is dictated by engine size and how much trouble and expense the builder goes to in putting the engine together. The name on the valve cover doesn't matter as much. I think you can get just as much power and reliability out of a Ford engine as a Chevy, you'll be ahead on originality, the car will look and sound right, and you won't have to keep answering questions about why you made the choice you did.
Like I said, it's only cars, as much as I love them. But if you want to swim upstream, there are very likely better streams to swim up against the current.