A very small amount of handlebar movement will give a set amount of bank, if this is enough for the turn, hold steady until it's time to straighten up, so the answer is yes. The bike is in opposite lock all through the corner. To corner tighter( more banking) turn the bars a fraction more. To come out of the turn straighten the bars up.
I don't think of it as pushing or pulling on the bars but as turning the bars slightly left to turn right and slightly right to go left. Depending on bike and tyre profile the effect starts roughly between 15 and 20 mph.
It's caused by the front tyre falling over a little as the bars are turned. So if, while traveling in a straight line, a slight pull is applied to the left hand bar the bike will bank a little to the right as the wheel falls slightly to the right (caused, I think, by the shape of the front tyre) and start to turn right. It doesn't continue to turn harder and harder unless the bars are turned further round, a little movement for a little turn, more movement to increase the angle of bank and hence turn tighter.
This is where the "counter steering" term comes from in that you turn left to go right. There is no need to move your body weight around, you can sit there like a sack of spuds and do the turning with the bars. It's a very sensitive thing, you can increase or decrease the lean angle by a degree or two at a time.
If you try it do it very gently to start with.
I read about it in a bike mag years ago and told a friend about it. Next time we were out on a clear road he started to weave back and forth across the road, he had remembered about it and was trying it out.
If this is not clear enough say so as I'm finding it hard to get something so simple into words without rambling on and on.