I would think "dropping out of warp" would be the same whether the escape is inside the ship or not.
I think of warp travel as just passing through another layer of subspace, so ejecting an escape pod at warp would be like a submarine ejecting an escape pod -- it just floats upwards slowly until it reaches the surface, since it is no longer being kept at that depth by the submarine's engines and weight.
Likewise, an escape pod ejected in subspace will float "upward" until it reaches the "surface" of space. There's no reason why leaving the warp field has to be violent -- as long as the escape pod has inertial dampers, like the rest of the ship.
It's not like starships traveling at warp are going "fast," and certainly not "faster than light" (if that were true, then Data would not be able to see Picard, since he's traveling faster than the light reflecting off Picard). They are just shifted into another layer of subspace as a shortcut through normal space.
When we see starships "drop out of warp," they usually pop into space at a fairly modest cruising velocity -- they are not moving at fast Relativistic speeds and applying braking thrusters to "slow down."
"Warp" is more of a place than it is a measure of physical velocity. Therefore, leaving that place should not cause much trouble for an escape pod.