If I recall correctly (I can't check because I sold my trade), at the end of the arc introducing Damien Bruce says that he ran the paternity test on Damien and that one day he would tell Tim the results when Tim was ready to hear it. It would be terribly ironic if it turned out that Damien, who prides himself on his father, wasn't Bruce's biological son.
Of course, if Batman and the whole Batfamily has taught me ANYTHING it's that family has very little to do with genetic ties.
I'm interested to know why Tim feels so strongly about Bruce being alive. Was he given some sort of hint that I missed?