I haven't found a transcript or recording of the interview itself, but I did find a transcript of a different interview where the two spoke about this interview:
Neil Gaiman: "The first radio interview we did in New York, the interviewer was asking us 'Who is Agnes Nutter? What is her history? Is Armageddon happening?" and so on and so forth. After a while, we twigged he hadn't realized this was fiction. He thought he'd been given two kooks who'd come across these old prophecies and were predicting that the world was going to be ending."
Terry Pratchett: "Once we realized, it was great fun. We could take over the interview, since we knew he didn't know enough to stop us."
Edit, later. Here are some more links confirming that this occurred (stolen from this answer to a very similar question on SF&F.SE): a mention of the interview in a reprinted edition of *Good Omens, a mention of the interview on Neil Gaiman's blog
Also, here's a quote from a Neil Gaiman interview in 2015 (which I found in the SF&F duplicate):
“[Terry] said ‘Well, you remember we were on the Good Omens author tour in February 1990’ … He said ‘We were in New York and we went to that ABC affiliate radio station, and the interviewer had not actually read the book … so when we started telling him about Agnes Nutter … we started explaining about this 17th century witch who all of her predictions were true … He did not realise this was fictional. We realised he had not read the book, and the engineers in the control room behind the glass panel who we could see and he could not, were lying on their backs kicking their legs against the walls.’
And I said, ‘Of course I remember. I was willing to let that go on for the entire interview’.
To answer the title question: Yes, this interview occurred. No transcript or recording appears to be available, however. (Also, go upvote Jos's answer - they got confirmation from Gaiman himself!)