But probably not in the way you are thinking.
I'm sensitive to chemical fragrances (which are often bad for you chemicals) so I only do laundry with "fragrance-free" detergent.
I can smell the detergent on other people's clothes.
Just this week, while I was running in the morning, I passed a teenager waiting for the bus by the side of the road. The wind is still, and it's a damp morning, but I can smell the detergent on him from 20 feet away!!
I bought an expensive sweater for cheap at a consignment store this week, and I can smell it from across the room - hanging in my closet! Another top I had bought I tried everything to get the smell out - washing, vinegar rinses, airing it out - and it still smelled of detergent (it finally wore off after about 4 months or so!).
Do you notice how strongly most detergents smell?? I HATE Gain - it's a nice scent, but it's extra strong and annoying.
Unless the scent is coming from natural ingredients, it's probably a cocktail of harmful chemicals. Chemicals that you are touching and breathing all day. :(