Of course if they listened to your conversation with your attorney the "fruit of the poisonous tree" doctrine would apply, but could you actually sue them if they did it? Do you have a right to privacy when interacting with your attorney?
Yes, one has a right to privacy in such a case
This right is clearly established, and so an officer or other government official or employee who listened in or authorized another to listen in could be personally sued under 42 US Code § 1983 often kn own simply as "section 1983). That law provides:
Every person who, under color of any statute, ordinance, regulation, custom, or usage, of any State or Territory or the District of Columbia, subjects, or causes to be subjected, any citizen of the United States or other person within the jurisdiction thereof to the deprivation of any rights, privileges, or immunities secured by the Constitution and laws, shall be liable to the party injured in an action at law, suit in equity, or other proper proceeding for redress, except that in any action brought against a judicial officer for an act or omission taken in such officer’s judicial capacity, injunctive relief shall not be granted unless a declaratory decree was violated or declaratory relief was unavailable. For the purposes of this section, any Act of Congress applicable exclusively to the District of Columbia shall be considered to be a statute of the District of Columbia.
The current version of section 1983 dates to 1979, but its hiostory goes much further back. This law derives from the Enforcement Act of 1871 also known as the Ku Klux Klan Act, Third Enforcement Act, Third Ku Klux Klan Act, Civil Rights Act of 1871, or the Force Act of 1871. According to the Wikipedia article about it:
The act was the last of three Enforcement Acts passed by the United States Congress from 1870 to 1871 during the Reconstruction Era to combat attacks upon the suffrage rights of African Americans. The statute has been subject to only minor changes since then, but has been the subject of voluminous interpretation by courts.
According to the same article, Section 1983:
is the most widely used civil rights enforcement statute, allowing people to sue in civil court over civil rights.
According to the same article:
A §1983 claim requires according to the United States Supreme Court in Adickes v. S. H. Kress & Co. (1970) two elements for recovery: (1) the plaintiff must prove that the defendant has deprived him of a right secured by the, "constitution and laws," of the US, and (2) the plaintiff must show that the defendant deprived him of this constitutional right 'under color of any statute, ordinance, regulation, custom, or usage, of any State or Territory' (under color of law)