Practically speaking, as a moderator - unless there's a specific request by a user or mod for CM or Dev assistance, its unlikely they'd look.
While I don't work for SE - as a moderator I've had to agree to a moderator agreement
Security – All records containing personal or financial information are considered to be our property and are afforded confidential treatment at all times. We work hard to protect against the unauthorized access, use, alteration or destruction of personal or financial information. All such electronic information is stored on restricted database servers, and is generally kept until such time as you may ask us to edit or delete it, as described below. We only disclose such information to our employees, agents or affiliates that a) need to know that information in order to process it for us or to provide other services, b) have agreed not to disclose it to others, and c) in response to lawful requests by public authorities, including to meet national security or law enforcement requirements.
So, practically anyone with access would need to have a need for it (so not the pastry chef) and agreed to not share it. Pretty sure this would be a NDA of some flavour. In any case, the personal information we have is limited and AFAIK there's been no incidents of mods or employees abusing it.