Hello, is it possible for an agent to switch to an off-queue state (such as Break) while on a call or chat, and somehow not hurt their adherence?

Only if they are schedule for that break when they change their status to break. Assume you want a delayed or pending status change, then the following idea I believe captures the platform related enhancement necessary: https://genesyscloud.ideas.aha.io/ideas/DIG-I-347