Acidburn,
I've looked at this too...and I don't see how it is possible. I know several people here on the forum do not use tensioners.
I've set up a few new bikes that, (just by luck), the pedal side chain and engine side chain were perfectly tensioned. The problem is that, as Tom pointed out, it doesn't last for long. A new engine chain will need adjustment almost immediately just like on a motorcycle.
Even with a decent amount of adjustment on the dropout, there's nothing you can do because the pedal side chain must also be tensioned correctly. If the pedal side chain was tensioned properly along with the engine side chain...the pedal side is going to remain correct as the engine side stretches.
The only bikes that I have seen with a decent amount of dropout adjustment have been single speed coaster brake bikes, or bikes with an internal planetary set for multiple speeds. In other words they do not use a chain tensioner...the chain is tensioned by the slot in the dropout so that the wheel can be moved back as the chain stretches.
A multispeed bike that uses a deraileur does not need a frame with a lot of adjustment at the dropouts, (it's for wheel alignment), the Deraileur takes up the chain slack.
The difference between a chain that is tensioned properly to one that is dangerously slack is less than one link.
The chain will not fall off when it gets slack...At the perfect amount of slackness the chain plates will ride on top of the sprocket teeth, and not fall off. The portion of the chain that is still seated in the sprocket will ensure that the chain will continue to ride on top of the teeth. In the first 5 degrees the chain will become TIGHT. In the next 5 degrees of rotation the chain will become REALLY TIGHT. After this the engine will be snatched from the frame, or the spokes will snap! It will happen too quick to prevent. On a motorcycle the rear wheel will lock up! On an engine powered bicycle there will be damage!
I have yet to do it, but I have an Electra here at the shop that has long slots in the dropouts for the rear wheel. I'm going to put a chain tensioner on the pedal side chain so that I can use the slots for keeping the engine side tensioned correctly. Correct chain tension is about 1/2" of up-down travel mid chain with the opposite side tight...just depends on which way you roll the wheel whether you're checking from the top or bottom. I prefer to roll the rear wheel forward and check the top, or drive side, of the chain...no reasoning behind it...just habit from MC days.
Without a great deal of fiddling around, and possibly a bit of expense, (high quality hardened chain), I don't see any way around using a tensioner for most bikes?
Jim