I've debated doing this before, but without spending the dough on the oil to match what you normally run, I think the benefit of "flushing" the dirty oil left in the pan is negated by having cheap oil replacing better oil...assuming one normally uses better grade stuff.
It depends on the vehicle though. Some engines have oil pans that are designed with the drain plug at the lowest point, and even angled for the best possible drainage, either with the front end jacked up or on ramps, or just straight down. There are lots of other designs where the drain plug is recessed higher than the floor of the pan, and some even have an internal bung with threads that sticks up in the pan more than a half an inch..which usually blocks any oil above that line from being drained. It makes sense to "flush" the pan, but still, even using a whole quart or two, there's no way it's actually flushing out ALL of the old oil, it's just mixing with it, and you can have a 25/75, 50/50, 75/25 or whatever ratio of new to old in there.
Similar to the transmission "flush" stuff, I have to say I think it's better to do ongoing changes rather than even dream of trying to get ALL new fluid in anything that isn't being completely disassembled. Changing the ATF every 33,333 miles probably beats flushing it every 100,000, both in ease of doing it yourself and keeping the lubricating properties up.
So in the same vein, I'd say it's "better" to either change the oil more often or switch to a better brand/type if sludge is an issue, or spend the extra quart money on getting one quart of premium synthetic stuff, and substituting it for one quart of whatever you normally use. The synthetic, even blended with dino oil, will clean up the engine some and hopefully help out with any sludge/buildup issues.
After that, the best thing you can do is change the oil HOT, right after shutting off the engine. The main reason being, all the contaminants are suspended IN the oil, so you're getting the maximum amount of "dirty" oil out. If you do a cold drain, most of the contaminants are settled at the bottom of the oil pan, and won't come out with the fluid that is left.
So basically, I'd say if you use good oil, maybe throw in a synthetic quart or synthetic blend once in a while (if you don't use synthetic already), use a good filter, and change the oil when hot, there will likely be little to no benefit do pouring in a fresh quart just to "flush" the system.
It would certainly be a heck of a waste to do that with a quart of oil at all, especially $5-6/quart stuff. I suppose if you're running cheapo $1 oil in an engine, and you either do cold changes or just get out a lot of sludge when flushing it, it might make more sense, but I think anyone who cares enough about an engine to use a quart of oil flushing it is unlikely to be using cheap oil or having oil sludge problems to begin with.
Overall, I'd think any benefit short of flushing out old oil from a cold drain is either minimal or non-existent. There is still LOTS of old oil in the engine after an oil change, and even the BEST oil is INSTANTLY mixed with it and turns dirty and black at the first startup. It's probably something mental for neat freaks that they think they are "cleaning" the engine out so the new oil stays cleaner longer or something.
