Usually yes. White is all 3 sub pixels (Red/Green/Blue) on at once. Red would just be red sub pixel so ABOUT ⅓ less power used. But to paraphrase akash.nu don't over think it and just use. If not getting a full day then start to look at ways to save power....so would the white face suck down more than the color one?
With that setup you’ll be fine. Even with the white background you’re not really using most of the screen real estate. Don’t worry so much about battery life. As long as it lasts the whole day you’re good. Just put it on charge when needed. Apple Watch in general is not made for going on week long camping trip without any charging options.