Well, apparently we'd still feel like the earth was accelerating at 9.8m/s^2 even if it was accelerating slower, because of the way Newtonian physics warps close to the speed of light.
Having said this, although it's theoretically possible, it's highly improbable that this is the case, as other weird things happen as we approach the speed of light
I argues the lighspeed point for a long time, and still can't get my head around it, but dysfunction provided a link to a physics forum which says it is possible.