Answer
No.
Work Step by Step
If the distance between the sound emitter and the sound receiver is doubled, the sound intensity $I$ is reduced by a factor of 4 (equation 15.26), which is the inverse square law.
However, as we see from equation 16.15, reducing the sound intensity $I$ by 4 does not reduce the sound intensity level $\beta$ by 4. The sound intensity level $\beta$ does NOT obey the inverse-square law.
