That is exactly what you should do. Start your activity on the Fenix and the HR will continue counting steps.
Most people I know do it that way.
The HR will continue counting steps if it is defined as your primary tracker. Just the activity will sync from the fenix and steps would be ignored.
I don't pay attention to it so I'm not sure about what would happen with calorie counts though. In the past, there have been posts in the forum about how Connect was smart enough to handle that and also posts about double-counting calories. Perhaps sopmeone else can answer that.
Obviously, the answer to your question about battery life would depend on how long your activities are.
Someone else might be equipped to answer.