I've done flushes with Dawn dish detergent before on my '88 silverado and I would bet the results are similar to simple green (which I'm HUGE fan of when cleaning tires and wheels). Since both foam up (the dish detergent more), you're going to want to use either a constant pump-type system or you're going to want to do the flush quite a few times.
... of course you're also talking to someone who ran water as a coolant 365 days of the year
Edit: I'd go with Jerry's suggestion. If it's a vehicle you REALLY care about, spend the extra bucks and buy the coolant flush for some peace of mind.