I have six out of the ten volumes of the series (1, 2, 3, 4, 7 and 10), and while I can't find a story that matches your description in any of the six volumes I have there is one that has some similarities. I'll describe it in case you've misremembered the details or maybe mixed up two different stories.
The story is The Man in the Gray Weapons Suit by Paul J. Nahin. It describes a navy pilot taking off from the carrier in his plane Red Striker Five, engaging the enemy then crash landing on the deck, just as you mention in your question. However this is not a drone and the pilot really is flying and indeed is seriously injured. The twist is that the pilot is so emotionally connected to his plane that he has come to love it as if it were another human.
The story ends:
The warrior smiled weakly through a pale white face lined with pain and shock. He looked up at Red Striker Five and saw not a technological marvel of electronics, armament, metallurgy, and computer programs. He saw both a warm and loving creature, and a being that had killed to save him. Killed with savagery and intelligence. His body filled with emotion, a feeling of passion that only later he would just barely begin to understand.
He looked at the battle-ravaged Red Striker Five, and just before he slipped into darkness again, he knew. He knew she’d be there when he came back. She’d wait for him, and he loved her.
And he knew she loved him too