"What would be the point of going to a musical if the person wasn't really singing?"
I know that parts of Phantom are pre-recorded, part of a scene in Wicked is lip-spoke and am pretty sure that other shows have done it as well.
However, this is only in small quantities.
David walked into the valley
With a stone clutched in his hand
He was only a boy
But he knew someone must take a stand
There will always be a valley
Always mountains one must scale
There will always be perilous waters
Which someone must sail
-Into the Fire
Scarlet Pimpernel