Yes, of course.
As with surrenders, the most important principle is to follow through on any commitments he makes; unlike surrenders, it's very common for untrained people to mistakenly make commitments that they are not in fact capable of keeping. For example, sometimes people will commit to not changing their behavior whatsoever based on information they learn, then discover that they aren't actually sure how they would have behaved if they weren't aware of that information. Even less expansive commitments, such as commitments not to reveal information in any way, sometimes run into issues with the fact that most people have imperfect control over their facial expressions, tone of voice, and so on.
The standard confidentiality agreement the Eagle Watch uses is "I won't willingly disclose this without your permission unless I learn of it unrelatedly, except to the Goddess." 'Won't willingly disclose' is generally understood to mean that the person making the promise won't tell anyone, won't deliberately communicate it through other means (including actions taken downstream of it), and will attempt to avoid giving it away through e.g. body language, but not to include a commitment not to be mind controlled or unwittingly mindread, nor a commitment to be perfectly capable at controlling facial expressions, actions that might give it away, etc. If someone wants additional reassurances with regards to the 'without your permission' clause, it's perfectly fine to provide assurances with regards to not securing it via mind control or other coercion, but Irabeth has generally found that offering those assurances unprompted is actually less reassuring. (Even without the clarification, he should still refrain from securing 'permission' via mind control.) In principle it's theologically permissible to conceal information from the Goddess, but in practice it's extremely hard to actually do so (although it's generally understood that if you have committed not to use it in a certain way, she will respect those commitments).
Lastwall confidentiality training includes lessons on providing more advanced or complicated assurances, such as committing not to use information that someone provides you against their interests, but doing this perfectly is generally understood to be extremely difficult.
There's some degree of tension between honesty commitments and confidentiality commitments. Irabeth's understanding of the orthodox position is that if someone asked Select Stasia (for example) 'do you know whether there are any former cultists in your congregation', she should reply with something to the effect of 'none that I'm permitted to disclose' whether or not anyone has in fact confidentially disclosed being a former cultist to her. In practice almost no one actually remembers to include caveats like that every time, but it's still good to include them at least some of the time so that including a caveat isn't equivalent to revealing the answer.
Questions about this?