I will like to know if 3d gamestudio support animation based movement. Where the position of your model is determaned by the current animation frame.

Where do you see the problem? Just pose the mesh and while the animation runs, let the entity stay at a static position. For collision detection you have to update the collision mesh each frame of course.

...which would be slow and laggy, i assume...

Depends on the complexity of the mesh... I am currently using such a techniqe for one of my projects and it works fine!

Do you have an example to show how it is performed?

i think he means, the animation it self will make the object move by its own, like you have a human model walking and the friction that the animation does with the ground will be the moving leadway.

imagine you have cylinder where the animation is rotating it , when you make animation based movement, the engine will make the object rotate by its own , no script here.
I think thatd what he meant.