Will it be possible to connect a Thunderbolt device to my USB 3.1 / C port?
Old-style, non-reversible USB "A" port (2.0, 3.0, 3.1 - lots of PCs and Macs): No.
Regular USB-C port (e.g. 12" MacBook, Chromebook Pixel, various phones): No.
Combined Thunderbolt3/USB-C port (e.g. new MacBook Pros, Dell XPS, various PC motherboards): Yes - but you'll need a TB3-to-TB1/2 adapter if its a TB1 or TB2 device - subject to PC/Mac driver issues.
Note: USB-C (the new reversible ones) and USB3-type-A (the old chunky ones that you have to turn around
twice to get the right way up) are
types of connector. USB 2/3.0/3.1 are
protocols that can run on either type of connector. TB3 is a protocol that uses the same connector as USB-C but isn't supported by regular USB-C ports. USB 3.0 is now called USB 3.1 gen 1 and USB 3.1 gen 2 is the new superfast USB, thunderbolt 3 can run over USB-C cables if they're less than 1m & thunderbolt certified, but USB 2/3 can't run over Thunderbolt 3 cables and DisplayPort can run over both but in subtly different ways, USB-C
might support DisplayPort 1.3 but TB3 never will and Chewbacca is a Wookey from Cashyyk but he lives on Endor...
Yup. USB-C will greatly simplify our data connections. Sigh.