Does it make sense to measure components in-circuit in order to prove non-functioning?
I always start with a good visual inspection for blown components and bad solder joints. For solder joints give special attention to inductors, transformers and connectors that may see physical stress. Next I start measuring in circuit without power applied. Especially identifying shorted transistors, diodes or blown fuses is easy. When a component looks bad, I go on and if it still looks bad I desolder it to check it again. Only when that fails to find the problem I either scrap the board (depending on how many I have of them) or I desolder more components to check them. Especially electrolytic caps are often bad; when they refuse to charge in circuit and measure couple MΩ out of the circuit it is fit for replacement. Also when they look deformed, replace them. 

I personally don't like powering up the circuit for measuring, but that is mainly due to the fact that the most circuits I repair are mains power supplies and those tend to bite when I'm uncareful. 

There is no right or wrong in troubleshooting a circuit as long as you are aware of what you may be measuring and as long as you don't blow any other components (or zap/hurt yourself) while you're on it.