Can I connect the FS3000 Air Velocity sensor to Raspberry Pi?

… without going through an arduino board first? My goal is to read directly using RPi I2C.

There should be no reason why not. You will have to adjust the library so it works on an RPI… but that does not look difficult.

Just be aware the board has pull-up resistors and so has the RPI on the I2C lines. So maybe you have to cut a link on the FS3000 board.