It is a little less risky to the quilt's unfinished seams at this point to just go ahead and finsh the quilt without washing. I mean, the inside seams are raw edges. So if you wash it now, you could get a lot of fraying and mess, and end up essentially ruining your quilt top. I guess if it were me, I'd finish it off without washing, and just resign myself to a bit of puckering later. As Porcelain said, sometimes the antique look can be nice. I personally don't like it for my own quilts, but that's just me. In this case you are safest just finishing the thing.
Since it has not been pre-washed, when you DO wash it, get a product called Retayne or other similar things. They are designed to stop the colors from running so much, and can be found at quilt shops and online. Or maybe the colors running would not be a big deal? Wash it on cold in any case. Watch out for reds and blues, they are the worst for running.