You can reply concisely and technically. Suggested answer:
No. Verification does not depend on the TimeProofs service being online.
A TimeProofs proof is a self-contained, cryptographically signed file. Anyone can verify it offline or with independent tooling by:
recomputing the hash,
checking the signature,
validating the timestamp against the public specification.
The service is only required at issuance time to sign the proof. Verification is intentionally decoupled to avoid vendor lock-in and single points of failure.
If TimeProofs disappeared tomorrow, all existing proofs would remain verifiable.