They were in the middle of the meeting when suddenly a naked man stumbled out of a closet and piled out of the room.
Is it natural to use “pile” as I have (similar to “dart”) when it’s only one person and not a group of people?
It doesn’t work, no. “Pile” is defined as:
a heap of things laid or lying one on top of another.
To pile out of a room really refers to a group of people exiting quickly or in a disorderly fashion, such that they appear to be in a heap on top of each other, or at least at risk of becoming so, perhaps stumbling over each other, etc.
It’s often an exaggeration, and can also be used to describe sheer quantity, for example:
They were piling out of the stadium after the concert.