Yes, that's the effect. But I'd only have to carry the generator portion when needed for a road trip. You could perhaps even rent it only when you need.
Even if the generator was in a small trailer, that would provide the range freedom without loosing the storage space (and help with venting/cooling/noise).
True, except the road trip case is also the case where you want more cargo capacity than is standard. A rental trailer for one week that lets my wife pack the kitchen sink actually makes sense.
Weight probably isn't a problem - a Chevy Volt weighs a lot less than a Tesla S.
You don't even save much by keeping the gas tank mostly empty when you aren't expecting to need it -- the gas weighs ~6 lbs / gallon, so you might save 50 lbs by keeping the tank on 1/4 when you aren't planning to drive past the battery range.
Think about it this way: batteries are really heavy, and the Tesla has like 5x more battery capacity than a Volt. Meanwhile, if you're mostly making short trips, you're hauling around 3/4 of those heavy, heavy batteries as a contingency.