light speed relative to accelerating & const vel source

[brightonb]

Two observers, A & B, are moving apart at constant velocity V. At distance D, B sends a pulse to A which arrives T seconds later. If B were instead accelerating at a rate such that he attains velocity V just when he is at distance D, and sends a pulse at this instant (while still accelerating but at velocity V), would the pulse still arrive T seconds later?

Thanks for any responses, Manny