In a general sense, if the 15 amp circuit is properly protected with a 15 amp breaker or fuse then it won’t matter what cable is connected. Having a 20 cable does not, in and of itself, increase current draw. You would have to connect devices that draw more than 15 amps to benefit Current wise from using the 20 amp cord. Of course if connected to a 15 amp circuit it will just trip the breaker or blow the fuse when it exceeds 15 amps, which is not really a good idea.
With respect to the 20 amp cable itself, The female end is unique since a 20 amp IEC is different from a 15 amp IEC. I’ve not seen the male connector (that plugs into the wall) on the cable you are considering, but there is a 20 amp plug with the return blade horizontal and the hot blade vertical. A 15 amp plug has both the hot and return blades vertical. I did a quick look at Music Direct and they had several 20 amp power cords from AudioQuest and Shunyata, none of them used the “special” 20 amp male connector. So you probably could use the 20 amp cable with your 15 amp receptacle.
Having said All that, as Brett recommended, adding a 20 amp circuit wired with 10 Gage wire would be the best thing you could do for your P20.