Yes, the 625 is built for 2 tv's. However, if your are currently using the PIP feature on your 625 with it in single mode, that will be disabled in dual mode to give you the ability to control each tuner separately.
As far as connecting the second tv, it has to be hardwired. What you may have heard about the "air" is the difference between the "air" vs. "CATV" method of modulation for the second tv to operate. If the house is already pre-wired for cable, you can use the existing cable to send the signal from the tv2 output of the 625 to your other room with your second tv. You can not use the existing cable in the house to connect the receiver to the dish.