Generally the ad network does not know if you really completed a purchase or dropped off during the funnel. Presumably advertisers could set up a hook to inform the ad network if you did purchase or not, but I guess they don't care enough to do so.
They may have improved.
I just bought a ladder on amazon, what information does that tell them? Since it's the only tool I've bought from them it doesn't tell them much. They now know that I might be willing to buy more tools from them in the future but doesn't help in targeting which kind or how often. Me being a ladder buyer is a very weak signal that I will buy any particular item from them.
If on the other hand, I've bought 15 Aubrey Maturin books from them over the last few months, it doesn't take the most sophisticated model to determine that I probably want to buy number 16 next. Or that I might like to read the Horatio Hornblower books.
The ads drove you to post here and as a result, I'm reminded amazon is an option for white goods.
It's almost as if, because it's rumoured to have powerful, dark & unknowable Machine Learning behind it, people assume it must be doing something reaaaaaally clever, and we're just not clever enough to realise what it's truly masterminding.