According to them, not necessarily [0]. They do have relay servers (they call them DERPs) [1] but they're only used in rare situations where UDP is blocked entirely.

I admit I wasn't able to understand most of those explanations so I could be wrong. :)

[0] https://tailscale.com/blog/how-nat-traversal-works/

[1] https://tailscale.com/blog/how-tailscale-works/#encrypted-re... under "Encrypted TCP relays (DERP)"