This is not done, but I couldn't find a definite reference for you. NASA has chosen not to publish recent ISS checklists. It's also hard to prove a negative, but for what it's worth, here is a fairly detailed sequence of events concerning a Cygnus departure from here.
Approaching the end of its stay at ISS, the S.S. Gene Cernan was
buttoned up by the crew – going through the usual procedure of closing
out the interior of the spacecraft before closing its hatch, then
outfitting the vestibule between ISS and Cygnus with bolt drive
assemblies and removing power and data connectors before closing the
Unity module hatch to permit the standard leak check to be performed.
Sixteen bolts were released to free the Cygnus spacecraft from Unity
and transfer control over to Canadarm2 that had grappled the
spacecraft on November 30.
Incidentally, some of the air is scavenged from the ISS airlock when it's depressurized for a spacewalk. The EVA OPS Checklist procedures 1.215, step 23 shows how a depress pump is used to pump the airlock down to 10.2 psi, sending the air back into the main body of the ISS. Further steps in the CREWLOCK DEPRESS/REPRESS CUE CARD part of the checklist show how the pump is then used to pump down the airlock to 2 psi. The final 2 psi is wasted into space.
I quote all this EVA stuff just to show that pumping down a volume into the ISS is time-consuming and requires special equipment that just doesn't exist at the CBM/hatch interface for the visiting vehicles. Furthermore, since the visiting vehicles arrive full of air, there is no loss incurred by letting them leave full of air. There, could, of course, be a gain if what you suggest was done.