No, it would darken. In general, sunglasses are used for prevent UV lights to protect eyes. The transition lenses could not be darken in the car due to the windshield of the car could block most UV rays. When the light come to transition lenses, there is no UV rays left. Therefore, the transition lenses just like general glasses thus they do not become dark.
The transition glasses will be changed the color when you go outdoors from indoors. The transition glasses will become dark when you are in the outside places. Although the function is a little like that of sunglasses which can protect your eyes from uv and strong light, you'd better choose the polarized sunglasses when you drive which may better filter the uv and bad lights.
Yes, transition glasses are very cool because they can adjust the lens color themselves according to the sun. In fact, the theory of transition lenses is based on UV rays. So, if you stay in convertible, the lenses can turn dark reacting the sun. However, if you stay in common car that prevent sunlight, your transition lenses probably won't turn dark because of no UV rays around the lenses.