Use of adapter to convert 15amp P/C to 20 amp IEC

IMO no. The unit is probably rated for 1600 watts max FLA connected load. That is why the 20 amp IEC inlet. I assume the reason you want to do this is because the supplied power cord that came with the unit has a NEMA 5-20P plug on the end of the cord and the receptacle you want to plug into is a 5-15R on a 15 amp branch circuit and 15 amp breaker. Just won`t fit will it.
It should work just fine.

Follow up, sorry my math was a little off. The max output load is probably closer to 1920 watts, 16 amps FLA, when using a 20 amp circuit. Just so you know you will now be limited by your 15 amp circuit breaker.

I would like to be able to use the existing power cords I have on hand (Harmonic Tech, Shunyata, Harmonix, Audience etc.)and experiment to see which one sounds best with the Balanced Power Tech 3.5. This unit has a 20 amp input IEC. I believe that all of these cords should be able to handle the power the 3.5 needs. It's rated at 2,400va. I quess as long as the cords have a 20 amp capacity I should be okay?