Does a hard drive need to have an external power source to be compatible with the Wii U?

According to Nintendo support, a dedicated power source is not necessary, but recommended.

Can bus-powered hard disc drives be used with Wii U?

Some bus-powered hard disc drives draw more current than the USB 2.0 specification and might not run stably, so we cannot guarantee that such devices will run properly on Wii U without the use of a supplemental power cable called a y-cable that draws power from two USB ports. For best results, we recommend using a external storage device with its own power supply that connects to the Wii U system via the USB port on the console.

Emphasis mine.

From the above quote, it appears that although the use of a y-cable is already good enough, you might still encounter a drive requiring more power than even two USB 2.0 ports together can officially provide.