That's the way it's "supposed" to work, but judging by the reviews on both Apple's own website and on Amazon, (two and three stars respectively), it's not doing so well.
There is however, the Cable Matters Thunderbolt 3 to Thunderbolt Adapter that gets high reviews though (IMO) is not as good looking as the Apple design. Though for me, it could look like a brick as long as it worked.
That said, generally speaking, I don't like converting signals, it's just another potential point of failure; instead I like going from "native connection to native connection" so it not only reduces the number of physical conversions, but the protocol conversions as well. While this will be a sore spot with many of Apple customers that invested heavily in adapters for their previous generation MacBooks, the consensus is that USB-C is here to stay.
Your best bet is to put those older adapters up on eBay and get new ones.