The only problem with testing components without removing them is that other components elsewhere on the board may, and often do, interact with the reading. Capacitors are even a little bit more tricky, because first of all, only more expensive testers can directly test capacitance. Second is that most testers that do test capacitance don't test them under load. It may look good on the tester, but once loaded down, might be a different story.

Usually when a capacitor goes bad, it won't test good with a capacitor tester. A lot of times caps short out, so you can use an ohm meter or diode tester across it. If it's shorted, it's bad. BUT if it's not shorted, that doesn't mean that it's good! )