The short answer is no. Some cards come with several backs and some come with few. In order to complete an entire front run, you will need to include a few different back types. That being said, I know several people who are putting together just runs of one back (Sovereign, Polar Bear, Cycle, etc.).
If you want to see which backs come with which cards, please go to
http://www.t205resource.com/
There are great checklists there.
Joshua
PS The minor leaguers only come with Hassan 649 and Polar Bear.