I have mixed mediums with no problem just like making a tee shirt quilt, make sure you use a light/ or shirt weight stabilizer on the poly and then treat it like any other fabric. The stabilizer will reduce fraying. and slipping. Also on the poly I would pink the edges when cutting to also help reduce fraying. If you are worried about seams coming apart between the poly and cotton seams, do double stitching on those seams.
Wash all the cotton before starting. I would wash the poly too, just because I do that. The poly will not shrink like the cotton.
I would also use cotton thread or a blend, whatever I have on hand.
good luck and please show us your progress as you proceed. Very interested to see it.
peace