To answer the title question, Yes you can be a software developer with an associates degree or no degree or an unrelated degree. I certainly would hire a person with those credentials if I felt they were good to work with.
The main places where it will be more difficult will be government work or large famous companies. Government jobs often use academic achievement instead of bothering to examine a person's ability to perform the job. And to work at Google, you probably need to get an expensive education or have already created a wildly popular web library. In general you might sometimes get unfairly pre-screened by recruiters if they are getting a lot of other candidates with more experience or a higher degree. (Eventually, that problem solves itself as you get more experience.)
But I think a lot of places are just interested in your ability to do the work. I have both hired and worked in other places that hired people with associates degrees (or no degree or unrelated degree).
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To answer the title question, Yes you can be a software developer with an associates degree or no degree or an unrelated degree. I certainly would hire a person with those credentials if I felt they were good to work with.
The main places where it will be more difficult will be government work or large famous companies. Government jobs often use academic achievement instead of bothering to examine a person's ability to perform the job. And to work at Google, you probably need to get an expensive education or have already created a wildly popular web library. In general you might sometimes get unfairly pre-screened by recruiters if they are getting a lot of other candidates with more experience or a higher degree. (Eventually, that problem solves itself as you get more experience.)
But I think a lot of places are just interested in your ability to do the work. I have both hired and worked in other places that hired people with associates degrees (or no degree or unrelated degree).