What business are you in and what did they propose?
It's promoted as a means of advertising, but I know others who did it. When the course ended, the students moved on to another school. So, basically you work for free with no long term returns.
Groupon didn't want us to so a short course, or a one-time discount.
There is a type of person that is attracted to Groupon - they are looking for the cheapest price, and has no brand loyalty. When the special deals end with Groupon, they move on to another company.
My wife discovered Groupon last summer. She has used it a few times, and it was always a one shot deal. Never went back to the same shop or salon because there was always a new shop offering a deal.
Another problem with using Groupon as "advertisement" is that only people who go to Groupon see the deals, not the general public. So, in effect, when you advertise on Groupon you are "preaching to the choir" in that you are pitching deals to Groupon junkies.