Cigarette ash absolutely gets sticky from tar. Source: worked in a casino for a decade, have seen dust built up in PC fans and any other airflow device or crevice many times that looks somewhat like fuzzy sludge. Fucking disgusting.

And yes all the beige curtains, walls, etc were white when we first put them in, matter of weeks for a brand new white curtain wrap(used to hide the poles for chandeliers that have camera arrays in them) to turn tan/beige