Possible to turn ON phone with ADB ? (Galaxy S6)
No, ADB requires the phone to be on and be running a OS/Recovery to accept it. The bootloader uses fastboot which is only available there. 

TL;DR No, when the phone is off it is not listening (by default, atleast) to commands from a PC.

EDIT: You may be better off jerry rigging something in it, is it the internal part bad or is it the external part?

EDIT2: People have pointed out that samsung does not even have fastboot (apparently) and that you COULD do something with a custom kernel, but that seems like alot of effort that may be better awnsered with get a rma or get a new phone, Sorry bro.