The danger is that your seams will fray badly.
If you are worried about setting stains in your completed quilt top with an iron, before quilting it, it might be wise to carefully examine your quilt top for stains, and then spot clean any questionable areas by hand first.
I had one old quilt top given to me that I didn't want to quilt without washing it. I filled up the bathtub with room temperature water and a little Synthrapol. Then laid the quilt top down in the water and let it soak for several minutes, and then gently swished it around with as little agitation as possible.
Then I rolled it between two cotton sheets and large towels.
Then laid it flat to dry on a bed under a ceiling fan.
When the quilt top was almost dry, I pressed the seams.
Then I blocked it and quilted it.
It turned out fine.
Judy Austin