According to the Washington Post Sept 25 2019 the answer (to the title question) appears to be: NO!
Below are excepts from that article that speak directly to the issue of "recordings" and the process by which "transcripts" are made:
Laurence Pfeiffer, a senior director of the White House Situation Room during the Obama administration:
White House conversations have not been recorded since the mid-1970s, when President Richard Nixon scandalized the practice.
Though audio of the calls is not recorded, per se, voice-recognition software [I think he is referring to Speech Recognition software like Dragon]is now used to help produce a baseline record of the call — almost like dictation — to get as close to verbatim as possible.
Pfeiffer said the software does not record or process the president’s voice. It processes the voice of a staffer who repeats what that person hears on the call. The software then produces a rough transcript.
(my comment: this is what one might see in a courtroom, where the court reporter is speaking into a microphone repeating all that is heard into a microphone)
At the same time, [Pfieffer] said, other officials listening in on the call, whether in the Oval Office or another meeting room, are furiously scribbling their own notes, as close to word for word as their shorthand allows. Those listening in could be the president’s chief of staff, the national security adviser or a member of the NSC staff in charge of monitoring the other leader’s region of the world, as well as State and Defense Department officials.
After the call, the note-takers compare their notes and consolidate a recollection of the conversation into one document, former officials said. Then it is passed to senior NSC staffers and other experts who listened, who compare it with their own notes and memories and also correct proper names and other errors the software made.
HOWEVER: “Don’t rely on whatever transcript is released,” said a former staffer, who spoke on the condition of anonymity to comment candidly. “Even if it’s unredacted; those transcripts are heavily edited by political leadership at NSC. I’ve seen substance deleted from these call ‘transcripts’ to delete either superfluous details or more substance.”
Finally: Pfeiffer said the note-takers’ raw transcripts were preserved during his tenure to protect the president against mischaracterizations of a conversation by a foreign leader.