Yes, it would! Fuel lasts about 30 days before it starts to oxidize. That basically starts to leave a gunk behind as the gasoline both oxidizes and slowly evaporates from the not-quite airtight tank. The fuel in the injectors evaporate and leave grime behind, clogging them, and this happens in many other places in the engine as well. The process starts after about 30 days, and by a year you're almost guaranteed to have fuel so rotten/sticky that the car doesn't start, or just barely generates power.
The Volt, BMW i3, and basically any other car with a range extender periodically run the engine in "maintenance mode", because it's good to circulate fluids, burn off some gas, and take some load off the battery for a while.
If you need to store a car for more than a month, you should top off and add a bottle of fuel stabilizer before driving home.
It appears that the Volt will detect the gasoline going bad (or at least, puts it on a timer and then assumes), and forcibly burn it off roughly once a year. Before doing so, it encourages you to use a bit of gas.
To be honest: this is the first link from a search engine. So its not an issue I've looked into very strongly. Nonetheless, it seems like GM has already figured out a procedure for "stale gas" issues.
That is a concern. I am a happy driver of a Chevy Volt, and in daily commuting only ever use battery. The practices I use to preserve gas in the tank for long-term storage are:
* Keep the tank full of gas: air space is prone to condensation
* Avoid ethanol-added gasoline, it's more hypro-philic
* Add a fuel stabilizer (like 1 fl oz per 5 gallon)
* live in California, it's really dry.
These are adapted from techniques for winter storage of cars.
I tried the steps you suggest, but on adding up the cost after a few weeks I found that, what with commuting from California to work, I was making a net loss.
Volt has 2 maintenance modes it automatically goes into
Engine Maintenance mode: haven't used the gas engine in some period (month?) so it uses the engine for a small period of time (less than my 12 mile commute) so get the engine oil moving.
Fuel maintenance mode: doesn't let average age of gas be over a year. i.e. I filled my tank August 30, 2017 from basically empty. On Aug 29, 2018 it went into fuel maintenance mode and even though I had a full battery, it would only use gas. I was probably around 1 gallon left, I filled it up, so expect around june 2019, it will go into fuel maintenance mode again unless I finish off the tank and fill it up again.
The Volt has something called "maintenance mode", which starts the engine about every 4-6 weeks, and does a process a little more involved every few months or so to burn gas that would go bad.
