Does the effect of gravity get slower at high speeds? If a sentient object was vibrating at near light speed and was some distance off the ground. Compared to being relatively stationary to the ground, would it take a longer while for them to fall down onto the floor from their perspective?
 A: You are basically asking whether an oscillating clock would run slower then a stationary clock on the surface. The answer is yes, because the velocity of the oscillating clock causes time dilation.

However we can answer your question very easily because both effects 1 and 2 make the falling clock run more slowly, so overall the falling clock must run more slowly that the clock on the surface.

Does a clock oscillating in a friction-free hole through the center of a planet run slower than a stationary clock on the surface?
Now you are asking about the duration of this trip to the ground viewed from the frame of the oscillating clock. From the oscillating clock's frame the trip takes very short time. 
A very good example for this to understand is the cosmic muon decay. Without this relativistic effect, the muons would decay and never reach the ground.

At rest, muons disintegrate in about 2 x 10-6 seconds and should not have time to reach the Earth's surface given there speed and travel distance. Because they move at close to the speed of light, however, time dilation extends their life span as seen from Earth so they can be observed at the surface before they disintegrate.

https://www.physlink.com/education/askexperts/ae611.cfm
Please note that you are asking whether this changes the effect of gravity, but both oscillating and stationary clocks are affected by gravity.
