Shop Elevator?

A snatch blocks increase capacity because it cuts the actual load lifted by the winch in half but require the winch to pull twice as much cable than if it was a direct pull. It is called mechanical advantage. The work done by the winch is basically the same if you neglect the friction in the pulley. Every extra supporting cable that you add, you increase the pulling force. In your drawing you essentially have two support cables even though there is only one actual cable. That gives you a mechanical advantage of 2 which in basic terms doubles the pulling capacity of the winch. I am not an engineer just a high school physics teacher so my explanation is by no means an engineer signing off using a snatch block to automatically double the winches lifting capacity in an elevator application but in a physics based explanation that is how mechanical advantage works. Your design functions the same as the snatch block picture you posted.