I am using timeline to run animations and various other features on my character during normal gameplay. I have noticed there's no gravity being applied during animations. I believe there's gravity applied normally via the Animator during root motion driven animations and is controllable via the gravityWeight Animator field (and via curves in animations by the same name). Is something similar doable with Timeline base animations?
Not really. If the animations control the root transforms, then timeline will always write it, even if physics/gravity is applied.