Nope, not really possible at all. The myth that Nero fiddled while Rome burnt to the ground has been pretty much completely refuted across all modern scholarship. He wasn't present in the city at the time of the fire; he was at Antium.

In fact, Nero would go on to help survivors of the fire in a multitude of ways , offering relief and reorganising the building limits of Rome. He took in the refugees and brought in grain.

Combine this with the fact that fires in Rome where common place, and what you have is a carefully engineered story created by critics of Nero (Suetonius, Tacitus and Dio are all equally guilty here) who wanted to further smear his name.

I just finished my dissertation on Nero in 62 AD, so I can give you some cool sources. Champlin writes particularly well on the fire, and also Griffon is worth a read. Any more details, feel free to PM