You absolutely can get on the throttle while leaned over. However, if you are at max lean and continue to add throttle without decreasing lean, you will eventually run out of grip and crash. The same is true for the brakes. Allowing time for weight to transfer to the front or rear increases your available grip and therefore the amount of brake or throttle you can use.
As for standing the bike up, I believe it is the same concept of how trail braking aids on turn in. When the front is compressed under braking, the rake and trail is decreased to a more sporty angle, which aids in steering. The reverse is also true. If you accelerate, you decompress the front and increase the rake and trail, aiding in stability and naturally making the bike want to run wider. This I know for sure, but does it actually force the bike off the ground on its own? I'm pretty sure every time I pick the bike up off the ground, I'm counter steering to do it, or forcing the bike to the side with my body. Take everything I say with a grain of salt, but my opinion is no, not by any appreciable amount.