A mom thinks her son could be raising another man's child. What advice would you give him?

Other People's Problems February 4th

I am having a difficult time with a certain situation involving my son (age 26), and his 30 year old ex-girlfriend with borderline personality disorder. (Wish I was kidding.) They were in a very volatile relationship off and on for 2.5 years. He broke it off with her back in June of 2012 and got back together with her in September of 2012. (She was seeing another guy during this breakup.) They both came to me near the end of September telling me she was pregnant (btw, showing already.) My immediate reaction was she was already pregnant before she got back together with my son. He broke it off again before the end of the pregnancy. They have not been together since.
 She has stated a few times that he’s not the father THEN turns around and says he is. Lately, she’s leading him to believe that he is the father of this baby. The baby is almost 9 months old.  She is the only one who really knows who the father is.  She has messed with his head so much and we don’t know if she’s ever telling the truth.  He is not on the birth certificate yet, but wants to be, if of course he is the father.  He is taking the child on overnights and helping financially and has bonded with the child.  Neither one is pushing this paternity situation, but I am.
This is where it gets ugly concerning myself being potential grandmother.  I have no problem with him raising the child of course if he is in fact his child.  I DO have a problem with him raising a child that isn’t his AND he isn’t with the mother. The other guy who is potentially the baby’s father DOES NOT know the baby exist.
My son wants me to bond with the child.  I do see the child regularly, but I never know from one day to the next if I’ll ever see the child again.  I have not allowed myself to bond to this child. Do I? Take on the baby believing that he’s ours (his son, my grandson) bond, buy things (set up house with baby toys), babysit as needed. Or, walk away till he gets this paternity test done. I have been pushing and pushing for the test.  My son pacifies me saying he on it and he’ll get one. Did I mention the BABY is 9 MONTHS OLD. Keep in mind that my son and I are very close (speaking several times daily.) but this paternity situation is causing a wedge between us. I think not getting the test is completely irresponsible.
Yesterday however, he said that he’s afraid that he’s not the father and doesn’t want to know and it doesn’t matter. For all intensive purposes he sees himself as father.  I think a test has to be done the other guy deserves to know if he has a child.  AGAIN, my son is NOT with the EX.
 As of yesterday we are not speaking.
Very concerned mother.