Is it possible to pursue ID in the scientific method???
Yes, just like it is possible to pursue astrology using the scientific method. Unfortunately for them, they both do badly.
Unfortunately, "ID People" tend to ignore these problems and proclaim victory
anyway. Occasionally they'll recant, but it often takes a lot of time and effort to get them to accept even rudimentary mistakes.
The 'scientific method' goes along the lines of...
Observe, Theorize, Test, Conclude
Is this the method followed by those who believe in and teach evolution???
Not usually by high school teachers, for obvious reasons. However, evolutionary biologists do use this method (though the method you describe is obviously simplified), and some of them teach at university.