Can I use a Canon Sigma Flash Gun on Nikon?

Will I be able to use my Canon fit Sigma EF-610 DG ST on a Nikon D5200?

The TTL function (auto flash metering) won't work as the Nikon won't recognise the signals.

I see no reason why it shouldn't work in manual mode (if the flash has one) as the common centre pin usually transmits the 'fire' signal. The camera may will likely need to be in manual exposure mode too.

Certainly I have no problem triggering multiple makes of manual flash (Nikon, Sigma, Yongnuo) using a 'Nikon' fit radio trigger on various makes of camera (Sony, Canon, Nikon, Olympus).

I wouldn't recommend it. They have different models of flash for different camera models for a reason.

At best you'd be able to use it in manual mode because the Canon flash won't talk Nikon so it won't respond to any of the camera settings or lens zoom.

No you can't. One understands Canon-speak, while the other only understands commands from a Nikon.
They are not interchangeable.

Maybe.

Voltage requirements may not be the same so don't blame me if something explodes.

You can definitely use the flash in Auto or Manual mode with the camera in Manual mode.