What will happen if I didn't supply the tavern with FOOD & Ale?

Without Food and Ale the population will drop. Not completely, but you will lose some. A lower population may slow down your gold production. This depends on the amount you are currently able to produce. You can check this by taping the gold value at the top of the screen to see the current efficiency.

There are also some upgrades that require a minimum population level to start them but once they are started the population can drop again.