May non-disclosures agreements between companies intrude on attorney-client privilege?
Yes. The attorney-client privilege may be waived by the client. See for instance, Goins v. Advanced Disposal Services Gulf, 333 So.3d 644, 653 (2021). Waiver can be explicit or implicit (Lacerda v. U.S., Dist. Court, June 2022, citing cases).
See also Center Partners, Ltd. v. Growth Head GP, LLC (Supreme Court of Illinois, Nov. 2012):
Any disclosure by the client is inherently inconsistent with the
policy behind the privilege of facilitating a confidential
attorney-client relationship and, therefore, must result in a waiver
of the privilege. [...] The holder of the privilege against disclosure
of the confidential matter or communication waives the privilege if he
or his predecessor while holder of the privilege voluntarily discloses
or consents to disclosure of any significant part of the matter or
If a company were to disclose something with an attorney that is under a confidentiality agreement with a third party, would it be possible for the third party to obtain compensation?
I gather that you mean disclosure to an attorney.
If the disclosure is strictly pursuant to an attorney-client relation and not released elsewhere (i.e., as in litigation using the records unsealed), the third party is unlikely to be entitled to relief. The third party would not even become aware of that disclosure unless the nature of his agreement with the company renders this type of disclosures foreseeable.
Is it good practice to have attorney-client privilege be something excluded from the definition of "confidential?"
It largely depends on how (if at all) the contract defines "confidential", other terms of the contract, and arguably also the context of that contract.
Where the nature of the contract does not entail matters typically protected by the attorney-client privilege, the wording for explicit exclusion of the privilege might inadvertently have an effect in the sense of everything which is not forbidden (that is, explicitly excluded from the definition) is allowed.