When using a swinging gate play - can the offensive center (long snapper first being an eligible receiver) shift to another position if they do not touch the ball (only aligning over the ball prior to touching the football if long snapping?
My understanding is this is a legal play in the NFL, assuming he was legally allowed to shift (he had not taken a 3 point stance or simulated one, but was in 2 point stance, ie, on his two feet).
From the NFL rules:
Article 3: Restrictions for Snapper. The snap (3-31) may be made by any offensive player who is on the line of scrimmage but must conform to the following provisions:
(a) The snap must start with the ball on the ground, with its long axis horizontal and at right angles to the line.
(b) It is not necessary that the snap be between the snapper’s legs, but it must be one quick and continuous motion of the hand or hands of the snapper. The ball must leave or be taken from his hands during this motion.
(c) The snapper may not snap the ball after it is ready for play until all of the officials have had a reasonable time to assume their normal stances. If this occurs, the ball remains dead, and no penalty
And as far as his eligibility to move, from earlier in that document:
Item 1: Interior Lineman. It is a False Start if an interior lineman (tackle to tackle) takes or simulates a threepoint stance, and then changes his position or moves the hand that is on the ground.
Item 2: Change of Stance. An interior lineman who is in a two-point stance is permitted to reset in a three-point stance or change his position, provided that he resets prior to the snap.
So if he was never 'set', he should be able to change position; and even if he stays over or near the ball, another player on the line may snap the ball (even, I believe, if he snaps through the other player's legs, though that's probably not a good idea.)
He could not move to an eligible position of course - he would have to stay on the interior of the line, unless he'd reported as eligible, in which case the initial formation might be illegal.
I'm not sure about college or high school, maybe Coach will know that.