You have two options. If you separated elements into layers in AI so you could animate the parts of the logos individually then the simplest option is to tie the extrusion settings from each layer to the other layers with simple pickwhip expressions so changing the extrusion depth on the master layer changes all the others.
If all of the parts move in unison then you can either parent them together or import your AI file again merging all layers and then convert the single layer to a shape layer. Now you have one element that you can extrude and animate.
If this were my project I would use the Classic Rendering comp setting, convert the AI layers to shapes, animate everything using flat layers, lights and cameras so that things look great except for the extrusion, then save the file, export the Comp as a C4D file, import the C4D file, and do the extruding in C4D Lite. You'll have a lot better options for extruding and texturing the layers, it will render faster, and you won't lose effects and blend modes that you have in a Classic 3D comp. It will also render a little faster and the work of staging and animating your animation will also be a lot easier. When you are done, you can even choose the Centered Comp Camera and change the camera move on the animated logo any time you like.
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