I think that CFR just just means that an “FAA student/solo certificates are not ICAO compliant”
Sensible answer is NO, but try your luck you get a surprising answers from NAAs if you push your case
Like saying can I fly solo in UK airspace with French Instructor Authorisation or DGAC issued Brevet De Base?
Or can I drive in France on a UK provisional licence and a 3 years friend sitting in the LHS?/RHS?
Can I fly PtF in France with UK NPPL? Can I fly German gliders in Morocco with UK BGA papers?
The meaning of the term varies between treaties and regulations. In the present context an opinion should be sought from the Office of the Chief Counsel for FAA. It has previously interpreted the requirement at 14 CFR 61.3(a)(1)(vii)—permitting a US-registered aircraft to be flown in a foreign state using a pilot licence issued there—as including licences other than those conforming to ICAO Annex 1. See final few paras in post 52 in the thread FCC radio telephone operators permit / radio station license. Solo flying training may be done with a US-registered aircraft in Canada under the provisions of NAFTA, under the direction and supervision of the holder of a Canadian instructor rating, so there is clearly a precedent although student pilot permits are issued there. See second para in post 9 in the thread N-reg in DTO? See also last para post 7 same thread.
Under your proposed interpretation of international flight much of the Chicago Convention is likely not to apply. I haven’t checked. Either way, the right of non-scheduled flight in a US-registered aircraft wholly within UK airspace is one established tacitly by custom as article 5 of the Chicago Convention does not apply. If the articles on pilot licences are not applicable then states would be under no obligation to recognise licences or certificates issued by the state of registry. The right to refuse to recognise pilot licences would not be limited to nationals of the state where the flight occurs.
The UK ANO does not offer an exception from the requirement for an appropriate licence to fly a non-EASA aircraft registered elsewhere than in UK to persons undergoing solo flying training. That is, the exception in article 140 applies to article 137 which covers UK-registered non-EASA aircraft. Article 148, lacking a similar exception, requires the person to hold an appropriate licence granted or rendered valid under the law of the state of registry or under the ANO. From exit day a UK resident will be required to hold an appropriate licence granted converted or rendered valid under the [UK] Aircrew Regulation. See licence maps in post 204 of the thread Brexit and general aviation, UK leaving EASA, etc (merged).
