Gradient meshes are not importable has editable objects in After Effects. The math behind them is completely different than any gradient in aftereffects.
An option is to stack up several different gradient fills with different blend modes in the shape layers. That is as close as you can get to having a gradient you can animate that has more than four colors.
It would help a lot if we knew exactly what you were trying to accomplish. The solution may be as simple as two different gradient mashes in illustrator and a simple change of opacity. Different blend modes between layers will give you even more options for a gradient transition.
as an example of what i'm trying to accomplish..
- imagine as Frame 1 we've photorealistic meshes of a person face directly facing the camera,
- Frame 15 is the same face meshes except as see from the camera obited 45 around the face Y (vert.) axis,
...what i like is to Blend between the meshes of frame 1 and 15 to produce the intermediate frames of the camera orbiting the face.
Without blending\tweening the meshes directly, morphing tween the "flattened" meshes is the only option i could find. These ofcourse are not live so can't be edited in real time and are far more labourious and problematic to morph between.
I would try some of the distortion effects that come with AE to change Morph between your two images instead of moving the paths. What you are trying to accomplish is quite easy using photographs. Treat your two illustrations as still images.
There are a lot of different tutorials on different morphing techniques.