It's on record that Karen 'previewed' her material with a number of people, including friends CJ and Debbie Cuticello, Frenda Leffler and her parents. What's not clear is whether anyone from the label ever asked for a sneak preview of what she was up to. I don't recall reading anywhere where that's been confirmed.
I don't recall having ever read anything about anyone from the label having heard tracks from the album before the playbacks in 1980 either. But doesn't that in itself seem very strange? This was a new venture with an artist who'd never recorded on her own now recording with a producer she'd never worked with before. Given A&M were putting money into the project (plus Karen was back in California more than once during the recording sessions), you'd expect Herb and/or Jerry to find out how it was going. It does beg the question of what exactly A&M were expecting to be recorded. Given Phil Ramone's style, the end result isn't that much of a surprise to my ears, so goodness knows what else they thought it was going to sound like.