You are mixing up terms. Autox does not mean track. Autox is in a parking lot and track is a road course race track.
Again, for autox it does not matter since it is at low speeds and there is very little risk of roll over.
For the track it really depends on the organization. For The Driver's Edge, who is really popular in Texas, the rules are outlined
here. As you can see the 370z convertible is allowed.