is there a way to store the generated mesh from a glDraw* call?

I have seen a mesh full of vertices and vertex information stuffed in VBOs and then rendered out with the glDrawArrays() call.

But can I store the drawn result from the glDrawArrays as a new mesh? The thing i am expecting to get after the glDrawArrays() call are interpolated vertices. so in a sense i have a denser mesh than the one i started out with - i.e. in the beginning, I just had the vertices that were used by glDrawArrays to create the 3d object.