Well yes, seeing as that's how you steer a bicycle. As a keen cyclist it annoys me when people (especially coaches) start harping on about countersteering being an additional technique you should learn, when it's what everyone has been doing intuitively since they first learned to ride a bike.
Counter-steering is said to be important to learn consciously because it's unintuitive, and people have crashed and died on motorcycles in panic situations by turning their handlebars toward their escape route only to have the bike go the opposite direction. Or at least I heard a rumor about that in my MSF course.
I do think it's valuable to know this fact consciously and not rely on body intuition, but I'm also sure it's much more important for motorcycling than for bicycling.
EDIT: There's a neat heuristic that was brought up in the course: the center of mass of the bike is above the bottom of the wheels, and a turning bike must lean into the turn (weird road geometries excepted), therefore to turn the stuff under the center of mass must counter the top leaning in. Thus to go left, you push left, causing the front wheel to pull out from under the bike right-wards, which starts to capsize the bike leftwards! Like I said before, a bicycle reacts really really hard to this, but a hefty motorcyle has a far lower center of mass and leans into it more gracefully.