Can you seriously say you would actually entertain those thoughts?
Yes. I genuinely, in good faith, would give due consideration to these claims for a few reasons.
1. Falma's previous mentor, who Palle holds in high regard as a rival, is also entertaining the notion of him being a pharmacist and vouching towards his authenticity.
2. To assume Falma dawns his credentials otherwise is to assume all other authorities around him, including both their father and the empress, are placating to his act.
3. Falma, although a 10 year old, is also capable of countering Palle's god arts and overpowering him. This calls into question how much he's truly grown since Palle last met him and the extent of his abilities as a god arts user. If he's capable of such an explosive growth in one field, why not the other?
4. Refer to the events of chapter 22. Falma has already demonstrated his ability as a pharmacist and a medical prodigy to administer an alternative solution to an ailment previously thought life-threatening, referencing things neither Palle nor his academic compatriots had so much as heard of. He accepted the excuse "it was from a book" then. Why not assume the same circumstances now?
I think that's where the heart of my issue with his character in this situation lies. He's disregarding something that should be core to his teachings and acting unbecoming of "a scion of pharmacists" from the esteemed Novalute Acadamy. He was vehemently denying Famla to an almost comical degree previous to the events of chapter 55.2 without any regard to the science he preaches. At best, it's unbecoming of his character and grossly hypocritical.