For entertainment purposes only:
Nearly anything can be done, though some things should not be. I am certain I could make or have someone make a custom intake manifold to run a 350 Holley. I don't think any of the MPFI manifolds on the Civics could or would be worth modifying to run a carb. The ignition may or may not be cooperative with the fuel injection disabled. You may get away with just running an MSD 6al box or the like, should you just need an alternative to the stock ignition module. You will need lower fuel pressure for the carb. A different regulator will likely not be enough. You would probably need a different pump, which would almost certainly require custom fitment to the tank. Even if you used an inline pump, you still need a pickup. You could switch to an aftermarket fuel cell, bearing in mind that it will require some custom work to fit to the car. You will not make as much power as the car does with MPFI, all else being equal, though you may get close. You will certainly use more fuel, and would likely have some trouble passing emissions. I think you would be nuts to actually do this, but it is fun to think about.