Absolutely. At least according to my own report from the past few nights.

After purging polyester from my wardrobe, I examined the bedsheets. They were 100% polyester. I promptly removed them and replaced them with our 100% cotton bedsheets.

With the 100% polyester bedsheets, I was never fully rested. I slept poorly, and I woke up often in the middle of the night. My wife would wake up, also, and often be unable to fall back asleep.

Once I changed to the 100% cotton sheets, however, we both slept soundly without waking even once. My sleep was so deep that my dream was an hour and half long and featured multiple acts. My wife also experienced detailed dreams, and she was surprised that to learn upon waking in the morning that she had slept undisrupted through the entire night.

What's so crazy about this is how fast it worked. Our sleep immediately improved upon switching to cotton. 

If this seems like a placebo effect, consider the reasoning behind why polyester bedsheets are so damaging to good sleep. The main reason one sleeps so poorly in polyester sheets is that polyester doesn't allow breathing. This means that moisture and heat from one's body become trapped inside the sheets, and it causes one to feel either too hot or too cold. It would be common for me, for example, to sleep with one leg outside of the sheets even on a cold night just to let some of the heat out.

If you find yourself sleeping with polyester sheets, switch to cotton and see if your sleep improves.