You could, I'm not sure exactly why you would want to, unless you need some special feature of the digital interface.

You would have to implement an SPI interface, which is supported, but with no real examples published. Doable though.

An easier (and cheaper) alternative would be to connect an analog k type thermocouple amplifier. Like this one:

https://www.adafruit.com/product/1778

Then you just need an analog input pin, and the interface is easy.

What is the temperature range you are reading? Do you need high temperatures (in the 1000 degrees range)?

Not without a lot of messing around (which was why I asked about the high temperature requirement).

Easiest would be to power everything from 3.3 V (or thereabouts) the modules can go up to 3.6V max, so you could run everything from a standard 3.3V supply/battery set up.

I haven't tried an SPI interface on a module, but I have implemented one on a cortex M1 before, and it wasn't hard (they have all the support built in).

I also interfaced an external break-out board to a module via I2C and had no real difficulties - if the SPI interface is as easy, then that may be the way to go.

You would be breaking new ground though, so be sure to let us know how you get on!