In Harper's biochemistry there is a sketch of "amphibolic intermediate products made of aminoacids' carbonic backbone". It shows through which different products aminoacids (not per se) are entering citric acid cycle.
In case of pyruvate carboxylase deficiency the conversion of pyruvate INTO oxaloacetate is impaired.
Therefore, as I understand correctly, all aminoacids, which enter citric acid cycle through pyruvate, would not be used in the process of gluconeogenesis. Of course the whole process would be impaired but for instance Phenyloalanine is entering the citric acid cycle through fumarate. That would mean that there is no need for conversion into oxaloacetate by pyruvate carboxylase but by fumarate and malate dehydrogenase.
I don't know if this question makes a lot of sense; it's quite complex and we wanted to take a look from different topics.