To understand the answer to your question, let me ask one in return: are modern psychologists able to diagnose people based on a second-hand or third-hand accounts of the actions of the person they are trying to diagnose? Would you be comfortable with yourself being diagnosed based on the accounts of people with questionable loyalty to you?

Psychological diagnoses are difficult even with the modern slate of psychological and physiological tests directly from the potential sufferer of mental illness. Trying to make a reasonably accurate diagnosis from someone else's accounts of their behaviour is basically impossible, even if we have some of their own writing such as correspondence to draw upon.

Now, whether it is meaningful depends entirely on your own subjective opinion. We don't need to take a judicial standard of sanity to make reasonable guesses or suppositions, as long as we recognize them for what they are. While considering historical events under a lens of "Person X was suffering from mental illness Y" offers us an alternate scenario with which to analyze their actions, as long as one understands that it is only supposition it can be a useful academic excercise.

Of course, the real problem of relying on second and third-hand accounts is that they might have no bearing on reality. For example, we can conclude, based on the accounts we have, that Caligula was either a crazy man or exceptionally cruel, because the surviving accounts do not give us many other options. But if we try to accomodate more than just the writings of people who hated him, as well as other evidence, we might come to different conclusions. Which is a more meaningful conclusion to draw?

No, the most meaningful thing is to keep in mind the limitations of the sources we often have to draw hard conclusions, and recognize the limits that time imposes on the 'truth' of history.