Jack, I wouldn't do that. I believe the voltage that powers the LNBs is higher than that which feeds the amp in the batwing. Might toast it.
See page 3 of the Winegard external dish manual
which shows how to hook a satellite receiver into the cable input of their receptacle for the batwing antenna.
In my '01, Airstream has already done this. The cable from the rear of the trailer comes forward to a plate that is hidden in the
rear of the credenza. That plate has two coax connectors. One is the cable from the rear of the trailer, and one goes up the wall to the center connection on the batwing plate.
Airstream ships the trailer with a short coax cable jumper between these two connections in the credenza, so the connector at the rear of the coach can be used for cable TV.
To insert a satellite receiver, you remove the jumper and connect the Sat In input on the sat receiver to one of the two connectors in the credenza, and the TV Out output on the sat receiver to the other of the two connectors in the credenza. It is possible to get them connected backwards, and I forget which is which.
Once it is hooked up correctly, when the amp switch on the batwing plate is out (OFF) the TV out from the sat receiver will be fed to both the coax connector on the batwing plate, and the
coax connector in the bedroom. When the amp switch on the batwing plate is in (ON) both its connector and the bedroom connector will get the signal from the over-the-air batwing antenna.
Hope this helps.