Yes you can put polyester clothing or any other polyester fabric into the dryer.
Just make sure that when you do put polyester in the dryer that you put it in the dryer on the cool setting because drying polyester on the heat setting could potentially melt the polyester and shrink it as well.
I dry the polyester on the cool setting in my dryer and it has never been a problem doing so.
However I once tried drying the polyester on the heat setting and the polyester shrank a bit and even began to melt some as well.
So yes polyester can be dried in the dryer but only if you use the cool setting.
Or even better you can hang the polyester out to dry which makes it even fresher and saves on your electric bill too.