This is primarily a North American concern. A 15amp 120V circuit does not heat water fast enough for the pre-wash cycle to actually have hot water in it. The wash cycle will eventually get hot water but not until at least halfway through, so for half of it you’re washing with cold/warm water at best. Depending on what you’re washing, that may be okay, but the dishwasher will definitely wash better if it is connected to the hot water supply and the hot water pipe is pre-filled with hot water by running the tap at the sink. European dishwashers are often connected to cold, because they have 220V+ heating elements that can deliver a lot more heat energy and they are designed for this. North American dishwashers are not.

The drain does not matter, you can pour whatever you want down the drain. The concern is on the supply-side only, and only applies if the dishwasher is in fact connected to the hot water line (which it should be, in North American installations, but sometimes it is installed wrong)