Sub-agent trees are fully tracked by the dashboard. When an agent is spawned, it always has a parent agent id - claude is sending this in the hooks payload. When you mouse over an agent in the dashboard, it shows what agent spawned it. There currently isn't a tree view of agents in the UI, but it would be easy to add. The data is all there.
[Edit] When claude spawns sub-agents, they inherit the parent's hooks. So all sub-agents activity gets logged by default.
[Edit] When claude spawns sub-agents, they inherit the parent's hooks. So all sub-agents activity gets logged by default.