The instructions that come with all window units tell you that the unit should be slightly pitched downwards on the side thats out of the window.

To more directly answer the question, yes most window units are designed to collect condensate water and use it to help cool the condensor. The rear fan typically has what's called a "slinger ring" around its circumference, which serves to pick up the water and throw it against the condensor (rear) coil. There's typically a hose or two or a drain channel molded into the bottom of the unit, leading from a collection pan beneath the evaporator (inside) coil to a pan beneath the condensor coil. In cases of very high humidity, the condensor pan can overflow, resulting in water in the bottom of the unit, which will likely find its way out through any slots or holes in the bottom, around screws, from side vents, etc. If one is handy and up to the task, a small hole can be drilled into the bottom (CAREFULLY, in a strategic location AWAY from the compressor and condensor coil -- one does NOT want to put a hole in them!*), and a catch-pan attached beneath the unit with a hose to divert the flow away to a specific area, away from sidewalks, flower beds, etc. My grandfather did this with a unit that extended over their back porch, so the water would drain out to the yard instead of across the porch.

(*One of my uncles attempted to drill a drain hole in a window unit many years ago, and put a hole in the compressor. I don't recall now if they had the compressor replaced, or trashed the entire unit for a new one.)

If you drill holes in the bottom of a window unit to drain it you defeat the purpose of the entire set up with slinging condensate onto the condenser etc. For the most part the condenser coil on many window units is to small so the set up is designed with a definate purpose. All the average homeowner has to know is if you pitch the unit the way its supposed to it won't back up into the room.

Not necessarily. Depends on how the unit is designed. If there's a "closed" drain system from the evaporator pan to the condensor pan, then only any overflow would be drained out through the hole(s). In any case, one shouldn't add a drain hole directly under the condensor if the pan under it is molded as part of the unit's bottom. If there's a separate plastic drain pan under the condensor, then *CAREFULLY* drilling a hole there (but NOT through the drain pan or the condensor!) to catch overflow might be the best location since it'd be the lowest point of properly tilted installation.

I recall Whirlpool window units with slide-out chassis that had a plastic spout to be installed in the frame for attaching a drain hose to catch overflow. Same concept.

Yes, a properly tilted unit won't leak into the room-side, but I don't think that's the question here. I'd recommend the OP not do anything unless leaking does occur outside and is objectionable in where it drips.