You'd have to be active to complete a checklist, whether on paper or not. So no matter how you do the checklist, I'd say that you're removing your attention from "looking out".... your looking out becomes more a glancing than actively looking.... and if you're actively looking, you're not paying attention to your checklist (paper or not), and your completion is just a glance where you don't see/interpret/understand what is in front of you.
The brain cannot do "two tasks at the same time", it can switch between tasks relatively fast though, but doing two tasks at the same time is more inefficient than one task at a time.
So better just place yourself in a situation where you can say "everything is safe for now.... time for the checks" and then return to actively looking out afterwards. It's way more efficient and safe for that matter.