I would say no, as the ability affects the shooting of the model, not the movement.
His ability to move is unchanged regardless of him having relentless or not; It's his shooting ability that is being changed. As such, if the ability is gone by his shooting phase, he's back to his regular situation and can only snapfire.
The only rules that would persist the way you describe it, is if it changes the units movement capabilities (move through cover, etc).
His ability to move is unchanged regardless of him having relentless or not; It's his shooting ability that is being changed. As such, if the ability is gone by his shooting phase, he's back to his regular situation and can only snapfire.
The only rules that would persist the way you describe it, is if it changes the units movement capabilities (move through cover, etc).