This is one of the exact use cases I have for my AirPods (that I have to stress I love love love, having owned most other types of Bluetooth headsets). I have a 2011 BMW 1 Series, that has the worst Bluetooth implementation for a car possible, it takes approx 20-30 seconds for the handover between phone and car, during this time I can't hear the caller and they can't hear me (and this assumes that it actually works).
Enter AirPods, that so far have had a 100% success rate of call handling.
Each AirPod is quoted as having 5 hours of battery life, in my experience this seems spot on. So if you were using one at a time (and this should always be the case in a car to meet most laws) you should be right for approx 10 hours (as one goes flat, just pop the other one in). You specific question about battery drain, I don't really know, but it shouldn't be an issue for most commutes.
That said, it's far nicer to return the AirPods to the charging case when not in use and this provides another 24 hours of charge (for a total of 34 hours use), this should let you get the following "active use" (assuming you start with full batteries all round), my guess is that in standby mode you would be talking triple this:
5 hours left, then return to charger
5 hours right, then return to charger
5 hours left, then return to charger
5 hours right, then return to charger
5 hours left, then return to charger
5 hours right, then return to charger
4 hours left, at this point both AirPods and charger would be empty
** Please check your local laws with driving with headphones/ear pieces, as you might still be breaking a law **