The use of composite materials for vehicle floor pans and/or aerodynamic undertrays is actually fairly common as automakers have been using both for some time now to increase fuel efficiency via weight reduction and aerodynamic improvements. As a result the exhaust heat issue is both well understood and easily resolved via the use of heat shielding materials. These materials can wrap the exhaust itself and/or be attached to the underside of the floor-pan and to the parts of the aerodynamic undertray which comes close to the exhaust. These have been proven to effectively dissipate heat enough to protect composite materials from damage.
So to answer your question the Elio exhaust will run under the vehicle along the right side frame rail. While you can't see that portion of the exhaust on the image below you can see the green exhaust running to and from the the right side at the front and back of the vehicles.
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