Yes you can tumble dry a polyester blanket.
When tumble drying polyester blankets or other polyester laundry make sure to use the low heat setting on the dryer so that it does not potentially melt the polyester blanket or other polyester fabric.
Tumble drying polyester should be done on the lowest possible heat setting and again, no more than 120 degrees F temperature and the polyester should be in the dryer without any other types of fabric and without other textiles or fabric softener present.
I tumble dry my polyester blankets all the time on the lowest heat setting and they've always been just fine.
However I turned the dryer up once before and it melted the polyester blanket some so just make sure to turn the tumble dryer heat setting down.