Unfortunately, this hasn't been my experience. As an example, I have a display-port-based Apple cinema display, and I bought this adapter to try to connect it to a new macbook pro 15":
http://www.apple.com/shop/product/MMEL2AM/A/thunderbolt-3-usb-c-to-thunderbolt-2-adapter
The physical size of the connectors are compatible, of course; you can plug the monitor into the thunderbolt-2-side of the adapter, and you can plug the thunderbolt-3-side of the adapter into the laptop. But, since the adapter isn't display-port compatible, no joy.If I remember correctly (and I might not), the apple store page for this adapter didn't originally carry a warning about this, but instead had text that made it easy to misunderstand whether this would work. The text on the page has changed.
As a weaker example, I have an LG 27UD88 Monitor. The USB-C connection from it works, but only carries 60W of charging "oomph," and the 15" macbook pro needs 85W of charging. So, even though the menubar icon on the mac signals that charging is happening, the battery is actually depleting over time. (Yeah, this one is more caveat emptor than the other, but still.)