Using the brakes while leaned over doesn't immediately stand the bike up. If you apply too much brake pressure it can stand up and cause you to run wide. But short of that, trailing the brakes alters the geometry and helps the bike turn.
Yes you can use the brakes while leaned over. I can honestly say there are probably only 3-4 corners in the entire Southeast that I don't trail brake into. Contrary to popular belief, the faster you go (lap times) the MORE you will find yourself using the brakes.
But as far as being leaned over and "grabbing a handful", no. That is never a good idea.
And even when straight up and down, the brakes should never be "grabbed". You can/should go to the brakes quickly, but it should be a smooth, deliberate action where you load up the front tire and then increase brake pressure.
Every heard the phrase "fast guys have slow hands"? If someone describes an aspect of their riding (braking, turn-in, etc) with terms like "grab", "throw", "toss", "jerk", "stab" or anything such as that, they are doing it wrong.