Pinout on a USB 3.0 connection to down-rate to USB 2.0
Yes, that looks correct from the connector perspective. 

Note that you should ideally pay attention to how you assemble a cable, for example shielding and twisted pairs for the D+/D- pins. 

A very short adapter is unlikely to have any effect, but a longer cable may play havoc with the required USB tolerances (e.g. max capacitance). 

You can buy inexpensive ready made adapters, which might be a good idea if this is a commercial product. Just search for “internal USB3 to USB2”.