In 2003 the Society of Cleaning and Restoration Technicians (SCRT) conducted a Water Extraction-efficiency Testing (WET) Study. This study paired different water extraction tools with different truckmount and portable vacuum blowers. Several types of carpets and carpet cushions were weighed, saturated, extracted and weighed again to determine how much water remained in the carpet and cushion after extraction. (1 800 949 4728 SCRT)
Every water damage class I have taken has always stressed remove as much liquid water as possible to decrease dry times.
Your are correct that there are too many variables to determine how much more drying time a poorly extracted carpet and cushion will take to dry. If you are drying a carpet and cushion "in place" or "top down" the drying time will increase significantly, blowing hot dry air over a carpet cushion and under a properly vented carpet, the drying time may only increase slightly.