Yes, once you reach your desired lean angle you would roll the throttle on "smoothly, evenly and consistently throughout the remainder of the turn" and you essentially release the pressure on the handlebars until it is time to countersteer back out of the turn. (from Keith Code's Twist of the Wrist II)
As for your question, I'd like to clarify it a bit here. There is a difference between countersteering TOO MUCH and running out of lean angle/traction and countersteering TOO FAST. I'm not sure which one you are asking about.
We know that it is important to get your bike turned quickly and at the lean angle you want asap so that you can get back on the gas. Keith Code says that provided the conditions are dry and you aren't using the front brake, you cannot countersteer the bike fast enough to simply tuck the front tire. Moto GP and top level racers are snapping the bike over fast and it is not the motion of quick steering that will tuck a front tire (in good dry conditions).
However, you can countersteer too much or kind of oversteer in a corner, meaning if you are making a right hand turn you could press on that right handlebar for too long resulting in the bike leaning over too much. (Body position and line play a role in this as well). The longer you countersteer through a turn the more the bike will continue to lean over farther and farther.
This ties into my original question about what to do once the bike is at the lean angle you want. Most riders think that they need to continue to "steer" or keep pressure on that inside bar throughout the entire turn but that is not the case. They end up leaning over too far or getting too far to the inside of the turn so they have to make mid turn steering corrections.
Get the bike to the lean angle you want and then STOP PRESSING THE INSIDE BAR.
Does this answer your question? How many times do you want to turn a bike in a corner?