It might, possibly. Energizing WiFi takes more energy, generally speaking, than a wired connection does, but I’d be surprised if you were able to see a significant difference. Probably less than 5 %, which given the Roam’s battery, isn’t much. Plus buying the adapter for a wired connection isn’t cheap, relatively speaking. 

I keep mine on the charger. In a past era, early NiCd battery systems tended to lose capacity if continuously charged and benefited by occasional full discharge. Lithium based batteries are the opposite. They love to be charged and don’t like to be fully discharged. 

My Roam 1 has been connected for most of its life, nothing untoward has happened so far.