Is an AFSP registration required for rotorcraft rating?
The problem is that person writing the FAQ seems to not understand the category and class system for pilot certification. The interim final rule (the actual regulation) does not make the distinctions you have discussed from the FAQ. See https://www.flightschoolcandidates.gov/IFR_Alien_Pilot.pdf as Category 3 does not specify an FAA pilot certificate category or class, just MTOW of 12,500 pounds or less, which means a R-22, R-44, Sikorski/Schweizer 300, seaplanes, gyrocopters, gliders, lighter than air, etc. unless specifically exempt elsewhere.

According to https://www.flightschoolcandidates.gov/TSA-2004-19147-0337.pdf the measure that they use with regards to whether or not you are subject to the "threat assessment" is whether you are taking training that will "substantially enhance piloting skills" but then it further states that the requirements are for the "initial pilot certificate, including a private, recreational, or sport pilot certificate."

It would be very hard to argue that training towards a certificate in RH is not going to "substantially enhance piloting skills". However, when they came up with the FAQ it appears that they have ignored that there is any category of aircraft outside of that of airplane (and any class outside of land airplanes).

Adding on RH (or Instrument-Helicopter) to ASEL/ AMEL/ Instrument-Airplane would be your "initial pilot certificate" in the rotorcraft category, helicopter class, or your "instrument rating" for that category.

For the sake of not getting yourself or your flight school in potential serious trouble, you should probably apply under the Category 3. If I were in your position I would omit the "probably" of the last sentence, but I am not a government regulator and I am not an attorney, so there is always a degree of uncertainty with regards to my personal interpretation of this material.