We have about the same size pool, also with a automatic pool cover. We have a heater and would not want to be without it, that's for sure. With the auto cover, it will keep the heat in better than without, but it's no better at getting heat in the pool than any other cover or solar cover.
Having a heater is key. It will extend the season if you choose to do so, but even during the warmer weather, it makes the pool so much more usable.
There were lots of times during the summer where it was nice out, but the pool just wasn't quite warm enough. This gives you control. You can choose to leave it be or you can choose to warm it up a bit. We're finding that everyone has a different tolerance for how warm they need the water. With a heater you can swim when you want, not when mother nature decides that you can swim by giving you the sun to warm the pool.
We end up keeping it on the warmer side because it is more comfortable for our kids and the guests that come over.
Just my 2 cents.