No, the halving won't reduce the supply. There's no way Bitcoin will reduce it's quantity, because it's always adding up regardless of how many halvings have done, but Bitcoin will eventually reduce the number of production in mining, thus making it slow to reach the max supply.
Also, it's not yet certain if the demand will increase this year's halving. Though one thing is for sure, there will be a possible scarcity due to high demand in the future when every piece of Bitcoin will be mined.