This was also a different news media at the time too, or at least not as tasteless as today's media can be, and at least pretended to respect certain individuals' privacy. They'd probably not cover it, at all. Unless she announces it on live television, or something, I doubt we'd know about it till sometime in the 70's or so.
Plus, as stated earlier, she'd have to prove it.
But if it somehow got out into the public, and she was able to, somehow, prove it, it'd definately be scandalous. This, again, was a different time period. It'd probably tarnish JFK's image majorly, maybe not get him impeached, but definately deflate the public image he had. This wasn't the 90's, where some people were like "Cool! My President's a playa!!111" when Bill Clinton's scandal came forth, a JFK sex scandal would probably rattle some things in the public consciousness.
You know damn well that guys like Kruschev would probably use this to mock the US a wee bit.