Termites, in our area of the world, eat only dry wood, ie. the structural frame of your house. Since the tree stump would be wet it will attract Carpenter ants, and many other thingys that help digest wood in the wild, but it is not likely that termites would move in there.

Yes, in this area. The stump and roots eventually dry out and become infested with termites.
We had several pine trees cut down many years ago and the roots still have termites in some areas of the yard. I didn't realize what the things were until they started eating any wooden stake I put in the ground.
I am now researching and trying to find out what can be done to get rid of them in and around my garden.