Is it possible that if a user has enabled the recovery feature, and has his/her data held by a third party, then it's probable that a government entity could issue a written order telling the third party to give them access to then user's coins/savings?

If you are a Recover user and have your shard into safeguarded by third parties, then yes, a government could subpoeana them and get access to your funds

Coincover will never pass your information to a third-party unless it has a legal obligation to do so. For example, law enforcement agencies often have extensive criminal investigation powers including the ability to obtain production orders requiring information to be produced. It may result in a criminal offense for any entity supporting Ledger Recover to fail to comply with a production order, but Coincover would always take all reasonable steps to verify a production order before complying with it.