Does Craft parse requests inside a conditional if it is false?
Yes, Twig will parse it all down to PHP before running it. It stores the rendered PHP in a /storage/runtime/compiled_templates/ file.

No, Craft will not run anything inside the conditional if it's false. At that point, it's simply processing exactly as normal PHP would.

So no, you shouldn't be notably penalized for anything inside a falsey if statement.