I don’t think so. The risk of a PR disaster because a car refused to start, due to them not having a signal either due to an outage, or being underground, is too great.

Car companies probably don’t want to deal with the headlines of “Man left stranded in parking garage after his car was unable to connect to the internet”, or “Woman marooned on mountainside because her car could not connect with the servers”.

At least, not until connection technology is good enough, or connectivity ubiquitous enough that neither of those are big enough issues for most.