Is it possible to turn off the sound when the charger is connected? I have got the answer from Sony Support that this is a "feature".
No. Assuming your phone is updated to Lollipop, the sound is just always on now.
You can switch to vibrate or silent/priority mode prior to connecting power to your device, it will vibrate or do nothing accordingly.
Maybe not the best answer but, try to change the ROM.
I'm using Resurrection Remix, so I can disable this sound and many other things. Like RR, other custom ROMs also have this option, such as Carbon ROM, AOKP, CyanogenMod, etc.
Try installing Setting Profiles Lite.
If you are rooted, you can get an Xposed module that can properly do that for you. And if you are really tech savvy, you can mod the
framework.jar, but that requires some coding knowledge and could seriously damage your device.