the seams will most likely hold up just fine.
still, i know how it feels to worry about a quilt's future if i don't have faith in the seam allowances. rather than toss the quilt, or hold onto the fear that i shouldn't pass it on to anybody else, i treat the suspect seams with a fray blocker. if i'm really worried about them, i glue the two layers of the allowance together with washable glue.
i wash every quilt i make before i send it on to test it for shape and durability. so far, none have fallen apart in the washer. :-)
if you also follow the suggestion to make sure the quilting goes over the seams for reinforcement, your quilt is sure to be a complete success. :-)