The 15-inch rule was originally added to the transducer installation instructions for those boats that have an inboard motor where the propeller is typically forwards of the transducer. The propeller can cause air to separate from the water and flow across the transducer which will not allow it to work.
Now if the transducer is mounted directly in front of the motor and/or propeller it can cause a problem in two ways: when underway and usually only at higher boats speeds, an air cavity can form behind the transducer which may not allow for proper water flow to the propeller causing it to slip or spinout. This air cavity if it reaches the cooling water intakes of the engine can cause overheating issues as well. Not all boats experience this and unfortunately the only way to know for sure if either/both of these will happen is to mount the transducer and test it.
As Rickie referenced though: you have to allow room for the full left-right turning capability for the motor too.