Can they expect the authorities to be kicking down their door in the coming days?"danblukk"
Depends on their paranoia.
Silkroad is up and running for already 3 years, they make several million dollars monthly by selling illegal drugs, and authorities still can't find them. So 100% protection with Tor is at least possible. Proven by this and many other examples.
But also there are some other examples, like massive de-anon with Firefox 17 exploit, which was done by NSA a couple month ago. So Tor cannot give you comfortable sense of security, you should still be on the alert, study known threats & ways to defeat them. Keep your software up-to-date, turn off insecure plugins, avoid careless behavior like sharing personal data etc.