Not sure what you are saying here? All proteins are made up of amino acids, and they only get converted into glucose if there is nothing more useful for them to do (ie repair cells).
I think you mean fatty acids here. In any case, being in a ketogenic state has less to do with what you eat and more to do with glycogen depletion. Its possible to enter a ketogenic state while eating carbs and no fats - its just a lot more difficult. You would probably have to go on a long distance run to deplete your glycogen, then you would enter ketosis and start burning your existing fat stores.
There is a difference between various amino acids. While most amino acids are glucogenic to some extent, proteins reserve carbon during metabolism, and the remnants of this are stored as carbohydrates via a process called gluconeogenesis, whereas the carbon remnants from ketogenic amino acids form fatty acids via fatty acid synthesis pathways. One of two things results: in the former, it results in synthesis of glucose or lipids, and in the latter as previously mentioned it results in energy via oxidation to carbon dioxide (and actually H2O) via the citric acid cycle.
Amino acids come in glucogenic, ketogenic, and a hybrid mix of the two flavours. Only lycine and leucine are entirely ketogenic as far as I can recall - the rest are glucogenic to some extent, and in protein this is certainly the case. So glucogenic amino acids result in the production of molecules that are the precursors to glucose via gluconeogenesis whereas ketogenic amino acids result in the production or net increase of acetyl CoA or acetoacetyl CoA, both molecules being purely ketogenic and are not precursors to glucose and are not subject to gluconeogenesis.
In short, not all amino acids are equal and protein does not only convert as a last resort, although one could theoretically say the same about most glucose in any case in people who don't suffer from type 2 diabetes or the metabolic syndrome...