Obviously the answer to my question is, "No," but I'd like to know why. My understanding of the twin paradox is that most of the time difference between the younger and older twin on a journey of 20 light years at a speed of c/2 or so is caused by the velocity that one speeds away from another. The rate of time ticks slower not just during the initial, turnaround, and final acceleration phases, but during the high speed constant velocity phase. So it's my understanding that relative velocity is the actual cause of the time difference, and acceleration is just a special case of increased velocity. This conclusion may be flawed, but it's the best one I can handle at the moment.
The conclusion implies that accelerated fields cause time ticking to slow down at an increasing rate. So a continuous accelerated field would cause time to tick slower and slower and slower. Gravitational pull is equivalent to a continuous accelerated field. So naturally we on a planet would expect our clocks to tick slower than someone out in space with a flatter space-time. I'm just wondering why our clocks in the Earth-bound gravitational field only go at a slower rate, but don't continuously slow down.