I wouldn’t think it would be admissible in any court.
The attorney-client privilege has a crime-fraud exception. Under the exception, conversations between an attorney and a client are not privileged if the purpose of the conversation was to discuss the commission or concealment of a crime. Generally, the client can prevent disclosure of conversations with the attorney by filing a motion asking the court to rule that the privilege applies and has not been waived by the client. Since Cohen is about to divulge information to Congress, and not a court, this might require the President to seek a temporary restraining order to enjoin Congress from proceeding. The President may not want to go down that road since it could require a hearing and an opinion by the court as to the likelihood of the President’s success on the issue. If Cohen does testify about alleged crimes, then, unless he invokes his right to remain silent, he may be implicating himself and could be exposed to prosecution if the statute of limitations has not run out.
The Democrats don’t care about what is admissible or even what is likely not criminal behavior. They merely want enough that the media can plaster on the front page, as well as discuss endlessly on news shows that will make the President “appear” to have engaged in misdeeds. It is ALL optics at this point. Especially now that he is out of the country negotiating with North Korea. They would rather burn the country down than allow him a win of any kind. And THAT is the scary part.