I'm considering buying a Canon XA10 and recording via the HDMI output onto the Atomos Ninja with the obvious benefits of getting a 4:2:2 color space and a higher bit rate.

The awkward HDMI port's location aside, I'm somewhat confused as to the type of signal that's output. The user manual states that the camera outputs 1080i via HDMI. But, I'm not clear as to what happens if one chooses to shoot 24P or 30P, for example. Internally, the camera can record native 24P in AVCHD. So how can one capture native 24P when recording via the HDMI port?

HD-SDI only supports a 1080i signal, so if you set the camera to record in a progressive format it will just embed that signal in a 1080i60 stream (it's called PsF for Progressive Segmented Frames). After it's recorded (or if the Ninja supports it, during recording), the progressive signal can be extracted from the interlaced signal to get regular 25p (or 24/30).

As far as I know, the Canon XA10 does not have HD-SDI.

I have just noticed that the XA10 webpage states:

HDMI Output (supports CEC, x.v.Color, and 1080p output).

So it looks like it will output 1080P. But, does that mean native 24P will be in a 60P wrapper? I don't get it.

HD-SDI only supports a 1080i signa

Since the OP asked about HDMI, that's irrelevant.

It's also incorrect. Both HDMI and SDI can support 1080i, 1080P and 1080PsF.

But that doesn't mean that any particular model of camera or monitor will support the format you want. I'd recommend you try to find the specs or user manual for the camera on Canon's website.