Conditional formatting can use values of fields. Fields are bound to controls. Some controls are drop downs. Yes, you can hide something based on the value of a field that is bound to a drop down. However, as I have been trying to say throughout this exchange - in order for your formatting to work, you need to know what the possible values of the field are.
So, if the values in the field bound to the drop down are 1, 2, 3, etc. but the display is "not started", "in progress", "complete" you need to set the conditional formatting to (for example) hide the button unless the field value is 3.
One way to find out the value of a field is to just put the field on the form - as a text field, or as a calculated value - so you can see the actual value when you change the selection in the drop down (for example).