Doubtful. Boarding passes contain a barcode with detailed and unencrypted information about you and your itinerary, though, so you should be cautious about where you leave them and shred/destroy them when you're finished.

But it seems unlikely that someone would find a random boarding pass and use the SkyMiles number from it to repeatedly harass a person like this without any motive. I'd expect the threat in that case would be more someone redeeming your frequent flier miles without your consent - and even that would require them to know your passcode or to convince a phone agent to make the booking.