Peripherals and the new Macbook's USB C system
Yes. The USB type&#8209;C plug has pins that directly connect to the USB type&#8209;A jack pins. If you have a device that requires a USB A port, then you can use the adaptor to connect the device to a USB C port on the Mac. Still, I would recommend checking to see if your Mac is listed as compatible at the link you provided.

I should point out there are many cheaper Apple compatible adaptors available, especially if the device requires USB 2.0. 

Basically, the adaptor just has wires connecting the plug to the jack.

USB Type-A Connector Pin Assignment






  Note: USB type-C plugs are reversible.


   Plug Pin Equivalence

Type A Plug      Type C Plug
-----------   ------------
VCC (VBUS)    + V
D-            D-
D+            D+
GND           GND
StdA_SSRX-    RX1- or RX2-
StdA_SSRX+    RX1+ or RX2+
GND_DRAIN     GND
StdA_SSTX-    TX1- or TX2-
StdA_SSTX+    TX2+ or TX2+


References

USB 3.0
USB-C
USB Type C 3.1 PD to get DC20V output