The car charger is an authentic AT&T Micro-USB Car Charger with USB Port 2Amp, so I guess that it would handle the spikes?
I just realized that my small Rosewill inverter has a USB 1Amp port, so it would probably handle spikes better than the above. Rosewill 150W Can Sized Silent Car Inverter with 1Amp USB Port RCP-E150C - Newegg.com