Why is an AN-24 hauling a US helicopter when US cargo pilots are furloughed?
Russian equipment has been hauling into Afghanistan for a long time. The US military can't handle the airlift; not by a long shot. ACMI carriers have been doing AMC airlift for some time, but have also been maxed-out for a long time.
ACMI carriers are private employers. The US government isn't employing the furloughed pilots. The US government isn't responsible for determining who is hired, furloughed, or how they're used.
Much of the equipment that's taken into Afghanistan is done through subcontracted operations. That is, a given company may deliver the freight to Dubai or Bahrain, where another operator may airlift it into Afghanistan, and yet others may move it around the country. Many of those operators are not from the US. AN-24 and IL76, and other equipment has been providing large volumes of airlift under contract to logistics operators downrange.
Some equipment goes on AMC commissioned flights direct out of the US to downrange locations such as Kabul, Baghram, Bastion, and other points, with intermediate tech stops as required. A lot of the material, however, goes to staging areas in the Baltic or the middle east, where it's redistributed before being reassigned to other carriers for the final leg(s). A LOT of operators and equipment s used to make those hauls.
A single helicopter isn't going to put pilots back on the line. Most of the ACMI carriers have been divesting themselves of certain types, such as the Classic 747s, resulting in permanent job losses for the FE's on that equipment, and in many cases, furloughs for the pilots on those types. Each of the ACMI operators hauls other things than AMC material. Each must be able to keep flying when the AMC flying goes away.
It's unreasonable to try to draw some kind of parallel between delivering a helicopter or load of ad-hoc cargo into Afghanistan, and furloughed crewmembers. It's far too simplistic and naive to think that one action is causal of the other, or that by changing the delivery of that helicopter to a US carrier, a company might recall pilots.
The truth is that among many of the carriers, there are more than enough crew members who are selfish and work plenty of overtime to make up for any losses of crew members to the street.