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See the documentation for the razor imu, section "Coordinate Frames" (You have to select indigo first):
The definition of the coordinate frame used by the Razor_AHRS firmware differs from what is printed on the board and also from the ROS coordinate frame. You will be exposed to these differences when testing the Razor AHRS and ROS topic output in the testing section below.
The Razor_AHRS firmware uses:
X axis pointing forward (towards the short edge with the connector holes)
Y axis pointing to the right
Z axis pointing down
Ignore the labelling on the board and use this coordinate frame when mounting the Razor.
So to answer your question, you are correct: