My second point based upon IO's reply - is that flight training whether done in a N reg or not - and whether done in the US or not will require a TSA approval if it leads to a FAA certificate and I do not think can be avoided as IO suggests.
Time to tear all my hair out. Actually I am sure this has been done to death here already.
Example: you do 50hrs in a G-reg plane here in the UK, with a JAA instructor of course. The intent of doing those 50hrs can be anything whatsoever; it can be a JAA PPL, it can be a Mongolian ATPL, or recurrent training without any aim whatever. Then you go to the USA; they
will accept that training towards the FAA requirements.
Are you telling me that you needed TSA approval for those 50hrs done in the UK?
As regards which FAA training doesn't need TSA (a separate issue):
This US AOPA link
http://www.aopa.org/tsa_rule/index
shows that below 12500lb these requirements apply only to flight training for a recreational pilot (applicable to US only), sport pilot (applicable to US only), private pilot (FAA PPL), instrument rating (FAA IR), or multiengine rating. A BFR, for example, is exempt. Training towards the FAA CPL is also exempt.
To paraphrase the foregoing, only "Category 3" requires TSA, reference
http://dmses.dot.gov/docimages/p80/310342.pdf
and this makes it clear that the Category 3 rule only applies to the initial Pilot Certificate (recreational, sport or private) the Multi-Engine rating and the IFR rating.
There is a further exemption for TSA for flight training commenced before Oct 2004, reference:
http://dmses.dot.gov/docimages/pdf90/300642_web.pdf