I have done these 6x for one airline that provided a fake SS# and they never went through (or they pulled the application like they said).
I did 3x for another airline, using my real info, as told to, with the understanding the application would be pulled. I got 2 of the cards and was denied on #3 because "I was already a card member". Took weeks of calling the mystery shop company to call the credit card company to get them cancelled. I never looked to see if it dinged my credit.
I recently took 3 more of those same shops. I used all my real info BUT I entered fake SS# on all three applications. I used three different numbers. Guess what? I got two cards in the mail and a denial letter for the third because I was already a card member. So the application was not removed as described, and I got two credit cards while using fake social security numbers. It again took weeks to get the shopping company to resolve with the credit card company.
I will not be doing these again.