You can't really say that without knowledge of how high those additional taxes would be. If the costs rise to the point that a reasonable profit for the level of risk involved can't be made then prices would certainly have to rise irrespective of demand. I suspect given the nature of ever rising taxation in most municipalities that introducing this tax even in a modest form would increase perceived risk[0] of property ownership enough to increase average rents.

[0]If the cost of an unoccupied property or a nonpaying tenant goes up, rents will likely go up in response.