As all good and bad in this world, it depends on the context of you story and your side character in question.
Is it funny?, Is it interesting? Does it give something extra, that is importan for you to tell in the story? Do other people whant to see it?
If most of that questions are yes, then maybe (just maybe), it will be a good idea to make more strories about the side character, as many have said, some side characters steal the show because how interesting they seem, and we whant to know more of them.
Or maybe they past is some how important to our current situation, (just ask the prequels of Star Wars that are made to explain who Dark Vader is).
At the end, if you are not interesting in the story of said character, and you are only writing more and more random thought over a character that you don´t actually care, the result of not doing something you care or love is ofter pure garbage.
If YOU think you should doit, go ahead, if you can make that character improve and mean something more to your story that just being a face in the background, sure then, go ahead.
At the end, the choice is yours, but you must make it.