"Can your son count? Mine can!"
Translation:Czy twój syn umie liczyć? Mój umie!
To some degree, yeah. But „móc” is not just about whether you are being allowed or not. It can refer to situation like you being able to get somewhere on time (because of traffic or weather), finding something misplaced, hitting something that moves fast (but you can use either, depending on whether you consider your skill or evasive movements playing a bigger role), health condition, etc.
That is a word order that is technically not incorrect, but sounds pretty strange. Kinda like "Is the person that can count your son?".
Basically, I wouldn't put the subject after a verb in almost any context. The two contexts where I know it works is Formal You and perhaps using "ktoś" (someone) in questions.