I prewash 99% of my fabric, including all my backing - and never had to iron any of it. I put a large 100% cotton towel in the dryer, dry on mid-low heat and take out as soon as it's dry, which isn't all that long.
I find with backing, ones it's washed it relaxes and is more straight of grain. Some of it gets quite stretched out of shape when folded at the factory.