I would guess that it will give you problems if you know that covering things with thick blankets doesn't help. I am sensitive to polyethylene but covering it works for me so I don't directly have experience to help you.
Build your own couch using materials you tolerate. Check anawhite.com --she has some sofa plans that use wood and foam camping pads which are often polyethylene, not polyester. You can make your own pillows with cotton batting
Buy an all-cotton fouton either sized for a couch or sized for a chair. I get mine from White Lotus. If you sign up for their newsletter they often have 30%off sales so the pricing is not too bad. That is also where I get my kids' beds.
XM,: mama to ds (5/08), dd (9/10) and ds (6/12) ! :C.H.S & M.