EDIT: Seems
Gramadach na Gaeilge contradicts what I wrote. From it I gather that synthetic forms are possible (and quite popular) in short answers.
Thus, you are right, “Labhraím.” is possible as an answer to “An labhraíonn tú Gaeilge?”.
I need to dig in Polish textbook for Munster Irish (
An Ghaeilge by A. Doyle and E. Gussmann), as I’m pretty sure it did suggest using analytical forms in this context…
EDIT2: And again my bad – it does suggest synthetic short answers, giving examples such as: “An dtuigeann tú?” “Tuigim.”, “An ndeineann sí obair gach lá?” “Ní dheineann”, “An nglanann tú an chistin ar maidin?” “Ní ghlanaim”, “An stopaimid anso?” “Ní stopaimid.”, “An bhfuil tú sásta?” “Nílim.”.
I don’t know where the idea of using only analytic form in an answer occurred to me then?

And you are right in both cases, certainly “Labhraím.” is a correct answer to “An labhraíonn tú Gaeilge?”, and “An bhfuil Gaeilge agat?” would be a more idiomatic way to ask whether someone is able to speak Irish.
I removed my old, wrong response.