It certainly is possible to transition. I know several developers who started off as English teachers, and then got jobs as developers. They had already studied computer science (or something similar) in university, or had previous professional experience as a developer.
Generally, I don’t think their goal was to work as a developer in Japan, but primarily to try living in Japan. After spending some time here, they decided they wanted to stay here longer, but not as an English teacher, and so found a developer position.
The JET programme is most common among the people I know, but there’s others who have done chain eikaiwa.
It sounds like you’re looking to come here as an English teacher, and use that as a stepping stone to find a job as a developer here. I can’t think of anyone I know who has gone down that route off the top of my head, but it might be a possible way as well.