Do a/c vents restrict air flow?

I just turned the air on in my house for the first time a few days ago and realized that the upstairs was a few degrees warmer then down stairs. I know this is pretty normal because heat rises and what not but I started to mess with the air vents and when I took them out of the floor there was a lot more air coming through. I didn't really test anything out yet but if more air is coming out with the vent off then in thinking it will cool the upstairs a lot better. Also the vent is so bulky underneath because if the fine you can adjust to direct the air. Could i cut all that bulk off and just be left with the cover?