Yes, Tesla's app would work just fine on an iPod touch (and an iPad as well). The caveats would be that the iPod touch and iPad would need a live Internet connection over WiFi (or cellular for the 3G/4G models of the iPad) and the iPad interface would just be the standard iPhone interface scaled up to the larger screen. The entry in the iOS App Store lists:
Compatibility: Requires iOS 6.0 or later, Compatible with iPhone, iPad, iPod touch. This app is optimized for iPhone 5.