I have a non-Energi model and I tend to let ICE kicks in before driving off....
Typically the ICE doesn't start until you are moving and keeping below 35mph isn't putting much stress on the trans or they would program it to start sooner.
Funny, you both talk like you have a choice... software upgrades don't allow it.
Every time you drive off in a cold C-Max, you can only use EV power. The ICE cannot be forced to provide torque under any circumstances, even though it is running. After about 15 seconds, the start-up mode ends and ICE begins to make motive torque. I first noticed it after the 2014 PCM upgrade, so I assume it's part of Ford's attempt to lengthen tranny life.
The easiest thing to look for is the charging state; you're discharging with the engine running in start-up mode. I drive uphill from home, so I notice a big increase in engine noise when it starts pulling and EV flips to charging mode. It's always near the top of the hill.
You can see it in one of Paul's video's, too....