And the effect of this on the acceleration of the spacecraft, as viewed from an external "stationary" oberver, would be???
;-)
I can't think of any, unless they could see the ship's clock, and note that (correcting for the message transit time) it's out of sync with the clock at home (assuming they were once in sync). Also, I suppose if the viewing position were right, they'd see a shortening of the ship's "forward direction" dimension (if you know what I mean). Offhand, I can't think of any visual manifestation of the increase in mass.