there are reasons i prefer to work with 100% cotton. quality is NOT one of those reasons. polyester is not inferior to cotton. it is merely different.
you have two potential issues to consider: (1) fraying; (2) shrinking
any fabric of any content can fray. that is your only real worry. use your rotary cutter to trim a straight edge at one end of the poly/cotton blend. sew a 1/4" seam along that edge and then toss it into the washer. check to see whether or how much that end frayed in the wash. turn the seam right-side out and tug on it a bit to see if it comes apart. if the seam holds then worry 1 is worry none.
as to the shrink issue ... do you plan to always hang the quilt to dry? if you do, then use the fabrics you have.
if you were planning to chuck it into the dryer, just change that plan.