I have done this at past companies and it only brought in 2 or 3 new reviews. However, I have also added this to the end of my NPS survey program for customers who gave us an 8+ and it did very well.
Mary Green Do you have their manager's contact information? If yes, I would reach out to them and explain the situation. A good manager will help diffuse the issue and/or get you a new CSM without complaint.