Re: heating return cut open
You want the conditioned air from the living space returning to the furnace, not unheated and probably rank air (unfinished basement ) from under the structure.
Will it negatively effect? Well, the furnace and AC will have to work harder to heat/cool the house because it's not recycling living space air. You'll lose more of your conditioned air when doors are opened because the house is pressurized due to less air being drawn out of the house than blown in. I would recommend repairing the damaged section.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!