You can do that. You just need to be aware of the differences between 65/35 poplin and 100% cotton. One is that cotton fabrics will fade faster over time, making the poplin colors more vibrant in comparison. (This isn't a problem if you are not making heirloom quilts.) Another is that poly mixes are harder to use with turned-under applique (probably not a technique you are planning to use). Check and make sure that the poplin doesn't fray more easily than cotton; if it frays very easily, you may need to go to 3/8" seams and choose patterns accordingly. Poplin is probably a little more slippery to sew; just be careful when you are sewing seams to maintain accuracy.
Having said all that, yes, I would sew a quilt of mixed materials including 63/35 cotton.