With enough fabrication, it could work.
It wouldn't work well though. Putting a large car engine into a Kart Chassis/Kart sized chassis will mean you will end up with a vehicle which will handle poorly, and will also be quite weighty.
The engine and gearbox will take up alot of room, as will the electronics to run the engine. You will also need some super strong suspension. Proper karts have little or no suspension travel, with the tyres taking up alot of the forces provided by bumps, cornering etc. So first, your going to need to find some good coilovers and tyres to handle this weight. Then, your going to have to find someway of weighing down the front, as the engine being at the back will cause understeer. You could either add ballast, or put the petrol tank there, but this will also cause understeer when the fuel tank gets empty.
However, while adding weight to the front may reduce understeer, it would increase the overall weight of the vehicle, further reducing the nimble handling that karts have. You would also need to think of some sort of drivetrain, whether you go for manual transmission/driveshafts etc, or rear sprocket/crank setup would be totally upto you.
And thats just part of it. All in all, it would be quite a hard swap and something which i would not reccomend. If you already have a kart chassis, then i would reccomend fitting a motorbike engine (something around 125-250cc should be enough) as the drivetrain would already be sorted as i believe karts already use a similiar drivetrain setup to a bike. The only thing you would need to sort out would be engine mounts/petrol tank etc.