Yes, oh yes! My kitchen looks like something out of the wild west sometimes, with balls of grey hair gently rolling around whenever there is a slight breeze or someone walks in! Bane of my life is dog hair.
I have a Henry hoover and noticed that my living room carpet was holding hair, even after a good vacuum, so have just invested in a Dyson. I have to say, I used it the first day I bought it and what came up from my carpet would shock you. The carpet looked clean, but I noticed that if I wore black and sat on the floor then hairs would stick to me. I no longer have this problem, my dyson is the best hoover I have ever bought and deals with dog hairs like no other hoover!
So, yes they do moult, but not sure about thinning, Murphy never thinned out, he just got bushier! You might notice that he thickens and crisps up more during the winter.