I would be wary of powering Tessel directly off of any kind of vehicle battery while the battery is still attached to said vehicle. Although Tessel can handle a 12V power input no problem, automotive power tends to be really, really noisy and rail voltages can experience gigantic swings depending on what's happening on the rest of the vehicle (for instance, running a starter motor or a particularly feisty alternator). These spikes could easily exceed Tessel's rated input voltage and destroy the device. Putting a linear regulator, like a 7805 or 7812, in front of Tessel would solve this problem.
The relay module is definitely only for powering other things.