Does i5 3570k come with pre-applied thermal paste?

Title is my question.

No, but the stock cooler that comes with the CPU does.

Im quite sure that all processors that come with a Heatsink have pre-applied thermal paste, I dont think the 3960X or 3970X come with stock heatsink/fans but thats because if you spent 1K on a processor youre more than likely going to be overclocking

The heatsink comes with the paste pre-applied, and if you buy an aftermarket cooler they will usually have a tube of TIM with everything else, the only time youll ever need to but TIM is if you buy something like a Waterblock or re-seat your heatsink to many times and run out of what was provided.