The whole idea that touching your face with your hands causes acne has been overstated. Touching your face with your hands, while not really helpful, probably isn't doing much to cause acne. And, more importantly, simply not touching your face anymore isn't going to make acne go away. The reason you have acne is not because you brushed your fingers across your cheek last week, and it's not even because you like to rest your chin in your hand.
The real acne-causing culprits are: over-active sebaceous glands (also known as oil glands), abnormal shedding of skin cells, certain bacteria (specifically propionibacterium acnes), and hormonal influences. Touching, or not touching, the skin isn't going to impact these causes all that much, if at all.
Of course, this all depends on what type of touching we're talking about. There are things your hands can do that will make acne worse. Picking at the skin, squeezing blemishes, and scratching off scabs will definitely make acne look worse. When you pop a pimple or pick at a blemish scab, you're creating more inflammation and damaging your skin. So, in that case, a hands-off approach is absolutely the best bet. But picking at the skin is very different than merely touching your face.
This isn't to say you you're now free to start touching and rubbing at the skin with abandon. Your hands aren't always the cleanest things in the whole world, so you may not want to be touching your face a ton anyway. And it's also a good idea to wash your hands before touching your face anyway, even if it's not to reduce acne. Hands can harbor germs. Touching your mouth, nose, or eyes with dirty hands can spread things like cold and flu viruses.
And if you're a bona-fide picker, it probably is best for you not touch your face at all. Once you feel a pimple, it's hard to fight the urge to pick at it, isn't it? In this case, it is so much easier to avoid temptation altogether by not touching the face in the first place.
Although touching your face with your hands isn't a huge acne-causing trigger, some things touching your face can actually make acne worse. These are items like sweat bands, hats, football helmets and the like. It's more about the friction, though, than spreading bacteria.
So you might not want to spend a lot of time with your face resting in your hands for just that reason, too. If you do this a lot (like every day during a boring class period) you may notice an increase in breakouts in that area. But again, this is more from constant pressure on the skin, not from a mere touch. And, for a lot of people, even lots of resting cheeks on hands doesn't affect acne one way or another.
But even if you were to never, ever touch your face from this point on, you'd still have acne. Because acne isn't caused by simply touching your face, acne can't be "cured" by not touching your face. Not touching your face won't stop acne.
If you want to see real improvement in your skin, you need to get on an acne treatment regimen. This may be over-the-counter products, but it might mean prescription medications too. A good daily skin care routine, a proven acne medication, consistent treatment and a bit of time will do the most to banish those breakouts, regardless of whether you are touching your face or not.