It depends on the failure, of course. However, I would say it's mostly not feasible.
If the semiconductors are going bang the answer is pretty much no. There is a very slight reduction in efficiency as the main transistors get too hot, but the difference is minimal until the moment of catastrophic failure.
For the output capacitors, you can likely measure ripple at the main switching frequency. An increase in ripple implies increasing ESR and/or decreasing capacitance. For the input capacitors, you'll see double your mains frequency (100/120Hz), though these caps going bad can also cause the PFC circuit to self-destruct. The 100/120Hz primary side ripple will likely only get really bad under high load, whereas the output ripple will likely be present under light load.
It's worth noting that while bad caps were a frequent issue 10 years ago, nowadays it seems like they are rarely the cause of a failure. Most power supply failures tend to be "bang and gone", or rare issues you couldn't spot beforehand (control IC suddenly breaking down, for instance).