If we could somehow "get off" earth, "stand still" and let it "float away", would time would appear to move faster?
A qualified yes, but it depends which time you mean by "time would appear to move faster". If you were "still", then those observed in motion would appear to have time pass more slowly.
Astronauts who spend time on the international space station age slightly less than people on earth (by 0.007 seconds behind for every 6 months) - time on earth goes faster than for them relative to those of us "stationary" on earth.
When two observers are in relative uniform motion and uninfluenced by any gravitational mass, the point of view of each will be that the other's (moving) clock is ticking at a slower rate than the local clock. The faster the relative velocity, the greater the magnitude of time dilation. This case is sometimes called special relativistic time dilation.
http://en.wikipedia.org/wiki/Time_dilation
(The whole Wikipedia "Time Dilation" article is worth reading)
There's nowhere to "stand still" in the universe. But if you pick a reference frame where you're moving less fast in space your velocity has more of a time component to make up for it. If you pick one where you move very quickly in space (maybe one that doesn't follow the Earth's orbit) then you have less motion in time. That observer sees you experience less time.
And if they pick a reference frame where you move the speed of light - where your velocity vector is fully in space; with '1' for space and '0' for time - they don't see you experience any time.
What I don't understand is: does this still apply under General Relativity, or does proximity to the massive earth redefine acceleration?