Do you get equipment back from dead soldiers?

In a normal play through, regardless of difficulty and/or Iron Man-ability, you will reacquire the former equipment of dead soldiers, even if no one makes it back to the skyranger.

In perusing the game's .ini files however, folks have found many references to a "Second Wave" mode, which is made up of optional elements that sometimes radically alter the gameplay.

One of these optional elements, "Total Loss", does exactly what you were wondering about - prevents the posthumous recovery of your soldier's armaments.

Unfortunately, you'll have to beat the game on Impossible to make it available as an option.