Judging from the reflection in the background, it appears that your sand bed is about 1'' deep. Is this correct?
If it is, then there will be almost no benefits from leaving it in place. To achieve any sort of denitrification effect you would need a good 3'' of sand. Given that you only have 1'', your sand bed is simply a detritus trap. As detritus accumulates, organic breakdown occurs, causing phosphates to rise and carbonates to deplete. This strains your alkalinity, calcium, and magnesium levels, requiring increased water changes to maintain a stable environment.
Because this is a fish only system and not a reef, I am making the following recommendation.
1) Remove the sand and replace it with aragonite. Use the smallest grain size you can purchase that will not be removed during water changes.
2) Place a power head near the bottom of the tank to circulate the water above the aragonite. This will help keep detritus from settling and allow your hang on filter time to remove it more effectively.
3) Consider adding a 2nd hang on filter to help remove this waste before it settles. It is extremely important to the long term stability of the system. Perhaps you can use a strainer extender to extend the intake near the bottom of the aquarium.
Finally, there is not a full view picture of you tank, so take this with a grain of salt.-) Make sure your Puffer has something to gnaw on. Small shells, artificial acropora branches, etc. The teeth of this fish grow very rapidly and the fish needs to grind the teeth to prevent this growth. Hobbyists who neglect this often find that long term success requires a visit from a dental aquatic vetrinarian.