You still need to send in all to due by April 15th.
The extension lets you get all the forms finished. You will get penalties for any amount short you were.
I see this “increase your exemptions and deny them money” idea before. It makes little sense. Come April 15th the account must be settled. They print whatever they want anyway.
But, the idea of filing more paperwork is a start. Changing exemptions is pointless because the employer handles that. But filing amended returns for trivial amounts will cost them. And if people turn in hand written forms the system would bog down, especially if the writing was poor or there were stray marks to confound the scanners.
The system relies on automation and computers too much now, it can be overwhelmed in a simple old-fashion way.