Why an early submarine charge might not sink a wooden warship

Would an attack by the American Turtle have been likely to sink a 64-gun wooden ship such as HMS Eagle?

No; wooden hull material is naturally buoyant, so a simple hole is less likely to sink the ship, though a successful magazine explosion could destroy it.

A metal hull stays afloat because enclosed air lowers the ship's average density, while the timbers of a wooden hull themselves tend to float. That makes ordinary flooding less decisive for a wooden ship, although underwater damage remains dangerous. The Turtle's charge was unlikely to work as intended, but an explosion that reached a magazine could still destroy the target.