I drive a 2014 Volt and have for 5 years. I mostly charge on my Level 2, and I've never had an issue with that except once, and that was not the fault of the charging method.
In 2015 I had a part specifically designed to step down voltage to charge the 12v battery fail, so the 12v battery died. Could have happened on gas, on LV 1, or LV 2.
I keep mine plugged on the 240VAC L2 40A Wattstation any time I'm not driving it, with the exception of using the included LV 1 charger now and then to make sure it is working. And, of course, I try to unplug it during the wonderful electrical storms we have here.
This lets me precondition in the mornings before I drive out into heat, bringing the AC loop (which is shared with the battery pack) down to 65F. I get phenomenal range this way.
Also all Volts after a software update sometime in 2014 I believe regularly test and top off the 12v battery when plugged in. Or should, unless you have a part failure like I did.