Does Detector Rail activate when an empty minecart passes over it?

All carts trigger the Detector Rails for now.

People are asking for wooden vs stone switch detector rails, but they are not in there as of yet.

Under most circumstances, detector rails will not care whether a cart is empty or not, and will trigger. However, if you put a detector rail on a slope (so the detector rail piece is angled) and the following section of track slopes the opposite way, the detector will not trigger for empty carts!

Bear in mind that detector rails on slopes are said to be a bit unreliable, and that this behavior may be considered a glitch and thus "fixed" in a future update!

Source: MinecraftWiki