You do realize you'll need to cool all the peltier with watercooling as well? Let's say you use some strong peltiers, 226watt for the CPU and GPU, that's 452watt of power from 12V rail already, and the amount of heat it's going to dissipate is going to be already 600watts+. To cool the water that you're going to use to chill the case, let's say you use another 2 226watt peltiers, and you have to insulate it perfectly, so with that it's going to be dissipating another 500watt+ heat. You're going to need a power supply stack, You'll need in total about 80A on the 12V rail, the best power supply out there can provide about 35A constant, so you'll need 3 600-800 watt power supplies.
So let's say you somehow insulate properly and no hot air gets inside the case, you'd better have a good way to cool your room because your computer is going to be dissipating over 1200watts of heat. Plus your power bill is going to jump.
And no peltiers can't cool CPU/GPU to negative temperatures, they can chill them to max of about 15C under ambient temperatures, depending on how well it is cooled. Now the radiator you mentioned that's going to cool the case may reach 5-10C, but the fresh air in the room isn't, so the temp is going to increase. Since your cpu and gpu is already being peltier cooled, then having a case with slightly lower temperature really isn't going to make much of a difference, but that'll be good for the motherboard and other components.
Don't bother with this, this is too inefficient, expensive and simply a bad idea. Best idea for extreme cooling is to simply use Freon cooling, then you can actually have your CPU in the -40C's zone.