Connecting Vcc pin to a logic gate
If there are no other input pins on the device, I don't see how setting the VCC pin to ground would cause any problem.  However, will the NOT gate provide enough output current to operate the device?  Note that many devices can draw power from input pins (https://www.youtube.com/watch?v=2yFh7Vv0Paw) and continue working even in the absence of a VCC connection.  But pulling VCC low while other inputs are connected may cause excessive current or damage.