Never, EVER do that, unless you're a psycho that don't think about the others and stupid enough to ignore that you can be one of the victims.
Of course, small amounts is impossible to avoid, for example washing a greasy frying pan. but NEVER, EVER, NO F-word way empty a fryer, for example, down the drain
It may not affect YOUR house, but it will definitely affect the public sewer system. It costs money to clean up "fatbergs" (and consequently makes everybody spend more money on utility bills)
It costs nothing to save the oil in a container and then dispose it accordingly.
Oil is also terrible for the sewer treatment and many times it can pass the treatment and end up in rivers or the ocean, causing a horrible environmental impact.