I believe that it might have helped her decision on the matter but I believe it was not the exact point. I believe that it was a number of things that helped Molly join the Order. I'm sure she witnessed several other family members and friends that their lives were claimed at the hand of the Dark Lord.

We also have to consider that Molly's heart is made of gold and she is one of the "good guys" in this series. She wants to do what is right and sitting back doing nothing is not part of her style.

I also believe that speaking of friends, all her friends were willing to join the Order and I'm sure that they only had to tug her arm a little to join their wonderful group. We have to remember that it was everyone for themselves if they were willing to stand up on their own and joining a group such as the Order, something that she would be interested in because it would mean protecting the ones she loves, would be the ideal thing to do.