I don't want to burst your bubble but animals can smell the faintest sent (ever seen a drug or bomb dog in action?). I do the above thing as far washing in sent free stuff. I do it to cut down on the smell. I do know that everything in the house goes throught it with Tide or whatever. The Dryer is no different.
I know that I can reduce my senct only so far. I take the furthur step to hunt where people are. I hunt suburbs to cover that dang sent. I like to hunt places that people frequent, I like places the have fires burning and places where heavy traffic flows.
If you want to take it to the extreme, wash in a spring, hang the clothes in the woods, wash with sent free soap and still hunt the wind...