FAA aviation accidents take months to years to get to the end. There's the preliminary report, the factual report and finally the probable cause report - I may have missed a step or two along the way. You can see about 50 years worth of stuff at
N T S B - Aviation Accidents - Index of Months

I'm guessing the FAA and NTSB could show up together depending on how close their respective offices are to the pilot and how "high profile" the accident may have been. Somewhat educated conjecture on my part, but I would not think federal agencies would do a good job of coordinating.

If it happened on the Appalachian trail, the state of South Carolina may be interested to know if our Governor is ok.

Good Luck
73M - Private Pilot, not an Airline guy.