Is it important to have proper ventilation installed when you turn your basement into living space?

This is very important to help prevent mold or odors from forming, most general contractors do not allow for enough airflow. To properly do this the contractor should know what the future use of the room/rooms will be and gather insulation factors along with applications. If they are putting in a green house then that is one application, if they have sleeping areas then that is another application. Several things will need to be confirmed before doing a proper installation.

You will have mold and major problems without hvac work.