Yes, if your motherboard specs says "USB3.1 Gen1", then it's a 19-pin header which is actually a USB3.0. Very few motherboard have the USB3.1 (labelled as "USB3.1 Gen2") internal headers, in which case you need a hard-to-find USB3.1-to-USB3.0 internal adapter cable.
USB3.0 (or "USB3.1 Gen1") headers are like this:
...which can accept your USB3.0 cable
USB3.1 (i.e., "USB3.1 Gen2") headers are like this: