Perhaps a bit of historical background would help clarify the relationship between Hold and Mountain Mode.
The 2011/2012 Volts had no Hold Mode. In Europe, the Ampera had City Mode, intended to enable drivers to preserve use of the battery for driving in Low Emission Zone urban areas that were being established, where use of internal combustion engines was either forbidden or subject to fees. The US had no such zones. Hold Mode first appeared in the US in the 2013 Volts. It allowed owners more control over when to drive on grid battery power. Use of Hold also complicated the tracking of Electric vs Gas Miles information as shown on the Energy Usage display.
What the US did have in 2011 was a very wide range of terrain that might be encountered by a Volt driver. As edk-austin points out, when the Gen 1 Volt is running on gas-generated electricity in high power demand conditions, it may need to draw power from the battery to maintain performance levels, returning it to the battery (by recharging) when demand is less. If the fully depleted battery cannot provide sufficient "borrowable" power, the car may enter Reduced Propulsion Mode until the demand is reduced. (The more powerful engine in the Gen 2 Volt significantly reduces this risk.)
GM, in effect, created a "Hold Mode hold point" at a predetermined battery state-of-charge level that would provide this sufficient quantity of "borrowable" power. They also implemented a "feature" that would allow the Mode to recharge the battery back up to this level if the battery soc was already below this level, or even fully depleted, before the Mode was chosen. This feature eliminated the need for a lengthy recharging stop before heading into terrain where the enhanced battery buffer may be needed.
Because the driving conditions under which high power demands are encountered are most likely to found when driving up long, steep hills (e.g., attempting to pass while traveling at freeway speeds up mountain roads), the Mode was named Mountain Mode. Under normal driving conditions, the Gen 1 Volt can recharge a fully depleted battery to the MM-maintained level in ~15 minutes. That’s why the manual says to switch into MM about 20 minutes before reaching the mountains. It’s also important to remain in MM (or Hold) until the final summit has been crested to make sure you have enough battery available for the final uphill drive portions of the trip.
Note that you may switch into MM at any time, even when the battery is fully charged, but if you do before the battery soc has dropped to the MM-maintained level, the Volt will remain in Electric Mode running on grid battery power until the soc drops to the MM-maintained level. At that point, the ICE will start and you’ll switch to using gas, and the battery soc will be held at that point, just as if you had switched to Hold at that point.
In GM Chief Engineer Pam Fletcher’s video discussing the 2011 Volt Drivetrain, she comments that it would be defeating the concept of minimizing gas use if MM was programmed to recharge the battery beyond the buffer deemed sufficient to maintain performance under high demand conditions. Most owners also find that it’s cheaper to recharge from the grid at home than it is to recharge using gas via MM.