Can articles published on academia.edu be regarded as scholarly publications?
It does not matter where it is published, it matters (as someone already commented) whether it went through the peer review process.

There are number of outlets to "publish" your work without peer review, the one I am most familiar with is arXiv. The distinction matters, because:


The research that has not been peer-reviewed may be of poor quality, biased, not up to scientific standards, or simply fake. Note "may be". Scientific conferences and especially scientific journals are assumed to do peer review before accepting the paper.
The review process is time consuming for the reviewers, so scientific community tries to prevent "double submissions" or even double publication. The "publications" with no peer review are not considered scientific publications in strict sense, therefore they are not counted towards "double submission" criteria (at least for the conferences I know).


So the answer is, yes, you can put it in your CV, but the reader may view it differently than you, e.g. the impression may be that you are unable to publish peer-reviewed paper, and resorting to this instead.

Now, specifically to Academia.edu, due to their model as "review along the publication, not before it" makes the point moot. But nevertheless, since you CAN publish stuff on Academia.edu without prior review, no one can be sure whether the work is of high quality or junk just by the fact that you managed to publish it. Granted, sometimes junk research gets through the peer review process as well, but there is reasonable assumption that the research is good, if peer-reviewed at a decent conference or published in a decent journal, while with Academia.edu it is fair to say it is probably exactly the reverse situation: one has to assume it is junk, unless proven otherwise by going to the site and reading the comments (if any).