Yes that is the gist.
The additional axis for lifting and lowering the head will need to be homed in some way. Either an endstop or stall detection against a physical stop, or manually setting position with G92.
Then the motion would be defined in the tool files. Which tool files you use will have to be worked out for your needs. Do you want to tool to drop into position when selected and raised when deselected? That will be up to you, I can only imagine since I haven't seen the mechanism first hand.