IF you balance the tiller in just the right position, with the right amount of tension.
Use two 24 inch bungee cords, or maybe less if your cockpit is narrow, and two pieces of 10 gauge solid strand insulated copper wire, like they use in a house for the water heater. Tie the ends of the wire to the post of the stern pulpit abeam of the forward end of the tiller. Afix the ends of the bungee cords to the end of the tiller, and make loops in the wires for the other end of the bungee so the tiller will be near the center. I made several loops so I could adjust the tension on the bungees and the position of the tiller by putting the ends in a different loop. Thus the tiller would be held in the proper position, BUT WITH SOME GIVE in both directions. I just bent the bungee ends to fit in the hole in the tiller for the tiller extension. To disconnect I just pulled the bungees out of the tiller.
Adjust the bungees so the tiller is slightly to windward, so that it will counteract the weather helm to sail a straight line.
To set the sails, get on the course you want and set the sails so that you will have weather helm. Leave a bit of luff in the main.
Now try to tie the tiller with the bungees to maintain this course, and instead of "course" think "point of sail". From a beam to close reach is the only place I could make it work reliably.
Sailing along, you have the normal weather helm pulling the tiller to leeward, but you set the bungees to maintain the course, so the tiller is slightly to windward.
1. Wind shifts to beam, a lift:
A lift will cause the luff to go out of the mainsail, and it will produce more power, heal, and weather helm. This causes the boat to turn upwind until the sail luffs again.
2. Wind shifts ahead (a header):
As the wind shifts ahead, the main luffs even more and power, heal, and weather helm is decreased, allowing the slightly windward tiller to turn the boat downwind (bears off). As the main loses power the boat heels less and two things happen. The tiller moves slightly more to windward and more of the windward hull is in the water, both help the boat bear off. As it bears off, the main comes back up to power, stopping the turn.
It's really quite fun to try, but remember if the windspeed changes your tiller and sail settings could be wrong! You can have it set perfectly balanced, and just a move to the other side of the boat and it won't be just right anymore. This is a way to give your arm a rest, not a way to leave the cockpit for extended periods.
Tying the tiller with two bungees makes it work infinitely better than just lashing it down, because it allows the boat to move the tiller by itself. You may have noticed an increase in pressure on the tiller when the boat heals over, this stretches the windward bungee and allows the tiller to move to leeward.
Once you have the boat balanced well, you can proceed to steer with the sails. By easing the mainsheet the boat will turn downwind a few degrees. Tying the tiller a bit more to windward will also change course downwind, and usually speeds up the boat.
To change course upwind, tighten the mainsail and perhaps reposition the tiller.