Funilly enough and if I remember it correctly, a pila is a kind of throwable spear from the Roman times.

You might be into something here. The spear is pilum, and Portuguese reborrowed it as pilo. However Portuguese used to repurpose the gender change for specific types of something, specially for Latin neuter words: see ovo/ova, casco/casca, jarro/jarra, barco/barca. It’s possible that the slang appeared this way, with people referring to their dicks as a type of spear. (It’s kind of childish but fairly common; c.f. caralho from caraculum “small mast”)

There’s also another Latin pila meaning mortar, but it got inherited by Portuguese as pia “sink”.

(IIRC pila-as-money is from a politician, Raul Pilla.)