Can anybody confirm whether or not I have to power down my 3750G stack before I add a new stack member or if I can safely add a new 3750G to my existing stack without powering the stack down.
No you just have to power of the switch to be added, here you are the steps:
Change the switch priority of the switch to be added to "1".
switch stack-member-number priority new-priority-value
Note: This step is optional, but it will make sure that the switch has fewer chances to become a stackmaster in the future.
Power off the switch that is to be added.
Make sure that the stack is fully connected so that, when you connect the new switch, the stack will be at least in half connectivity and does not partition.
Connect the new switch to the stack with the StackWise ports.
Power on the newly added switch.
After the new switch comes up, issue the command show switch to verify stack membership.
HTH, please rate if it does help,