The washers and do not washers are both quite vehement in their opinions.
I am VERY VERY VERY pro-washing. I know the quilts I make will have to visit the washing machine at some time, and I really don't want an unpleasant surprise after it's all put together.
I also don't know how finicky/careful the new owners will be when they do the laundry, either.
Some old machines still sew beautifully. Maybe a visit to the "machine doctor" might be worth the money.
Most piecing - as far as I know - is done either by hand with a very short running stitch - or with a straight machine stitch.
If you are sewing with a short stitch and stretching your fabric, that might cause puckers.
When I took a class ages ago to learn how to sew T-shirts, we were told to LENGTHEN the stitch and stretch the fabric - when relaxed it would lay flat and have some give.
When stretched and sewn with a short stitch, the fabric would just ripple. (And it would be very hard to unsew)