Hdd sends code to the ram. Ram ships it to the cpu when it can. The cpu decodes/processes that data 1 frame at a time then sends it to the gpu to paint the picture according to resolution and settings. Repeat. If the gpu is capable of painting that picture 60x a second, it'll demand that data from the cpu. Generally that's plausible. If the gpu is capable of painting that picture 144x a second, it'll demand that data from the cpu 144x a second. If the cpu can only decode and process that data 100x a second, that's all the gpu is going to get, no matter if the gpu is capable of more or not. The cpu could care less what the resolution is because the data is all the same, whatever coding the game engine has. To a cpu 4k and 1080p don't exist, that's all gpu. The only thing a cpu worries about is how many frames per second it can process and ship to the gpu. There are graphics settings that do affect cpus, such as viewing distance and grass detail, but only in so much as that changes the limits needed for process. Turn down grass detail and the cpu only has to send a green blur to the gpu to paint, max out grass detail and the cpu has to apply shape, motion, color details in far greater numbers. Fps tanks.
Fps is governed by the cpu. Resolution governs the gpu. The only relationship the gpu and cpu share in fps is the gpus ability to demand, whether that's lower or higher than the cpu can supply.
That said, to answer Op, yes your setup affects performance. But not ability, just the limits. For example, I own a Dell factory mass produced 2button mouse. It's near indestructible, old as the hills and still works great, it's on its 5th pc now. However, being only 2 button, it means my other hand has to spend more time punching keys, I must move the cursor around more to click on menus etc, when a multi-button mouse could have macros set to do the same thing. The most obvious is in 3rd person view, the scroll wheel zooms in/out on the view. With just 2 buttons, I have to let go of wasd keys, cross the keyboard and use the page up/down buttons manually. Constant dance. So a better mouse would increase my gaming performance, I'd Dodge faster, move better, have better zoom control for snipers etc. Same goes for mechanical keyboards, some are hard press keys, some are soft press, some have loud clicks, some are silent. If you have a soft touch, and fast fingers, a loud click/hard press keyboard will drive you nuts. Or if you have masher type hands and prefer to know exactly when the key is activated a hard press/loud click keyboard would be perfect.
So while absolutely Yes, setup affects performance, it's not so much what it is, but how it applies to you.