no, we would just approach it asymptotically, and we would also notice that as time goes by, everything gets heavier, and heavier, and heavier etc...
as time goes by, relative to zero movement, the effect of time on us would be getting slower and slower.
so when we looked at everything else relative to us (on earth), it would be getting faster and faster.
also, if the earth is accelerating at 9.81m/s upwards, then what is pushing it? a giant rocket or something?