Not necessarily. If landlords would rather keep their property on the market in the hopes of getting a higher rent price than lower the price then the price will remain static. There'll just be more un-let, empty properties. In the UK this happens a lot because property tax (council tax as it's known here) is discounted on an empty property, so there isn't much incentive to fill the property at a lower price.

The economics of the property market are weird.