The answer to the question is probably yes. However, it depends whether your state has a law that addresses grandparent visitation (and what that law says) as well as whether the other parent supports his/her parents being awarded this visitation.
A good starting point is http://www.enotes.com/everyday-law-encyclopedia/grandparents-rights. You will find in researching this topic that the courts will also look at the “best interests of the child,” so if there is something objectionable in the grandparents’ past, a court will take this into consideration. Also consider contacting your local bar association to meet with an attorney in your state. You can usually get an initial one hour consultation for free or for a small fee.