Have to have at least one in the backfield to receive the snap
Not true. There is no requirement for any backfield players. The snapper can snap the ball backward, let it leave his hand(s), and then other rules govern who can catch or recover the ball.
-If all 5 lineman are ineligible (and they would be, in this scenario, since they would be numbered 50-79), none of them could receive a hand-to-hand snap (not really sure how that could happen, anyway).
-When the ball leaves the snapper's hand, it is a backward pass, and any player of Team A (or B) may catch or recover a backward pass. How would that happen? The ball could be snapped high into the air, and one of the linemen could, in theory, turn and run to it and catch it. It could happen.
-If the backward pass from the snap touches the ground, any player of Team A (or B) may recover it. Easy to imagine that: ball is snapped straight back and falls to the ground and is bouncing around several yards behind the NZ, and an A player retreats from the line to recover the ball and attempts to advance (or just falls on it).
-Yes, there is rule regarding a "planned loose ball in the vicinity of the snapper," and that could come into play. Snapper snaps the ball backward but lets it fall 'softly' out of his hand, so the ball is just sitting on the ground immediately behind him, so another lineman can move along behind him, recover the ball, and attempt to advance. By rule, if he is able to advance the ball (fat chance), we could enforce the planned loose ball penalty. My guess is he'll lose yards, and get creamed in the process.
So, is 5 players for Team A (all linemen numbered 50-79) a sound offensive scheme? Nope. Legal? Yep.
Robert
(OK, things may be different for 6-player football, but I'm not an expert in those rules.)