I'm probably the wrong person to ask that question to, because if it comes to a question between writing and not writing, write. Always. I don't know about you, but I get crazy when I don't, so I have to assign myself little things to write about.
That being said, if it's not a question of whether to write, but a question of what to write about, you might find it an interesting exercise. I love giving characters more character development; it's something I do for fun because suddenly, a lot more comes out of the character than meets the eye. I do think that if you do it though, you're going to need to know exactly what is happening in the fanfiction to know what to account for. Don't be afraid to be flexible though; sometimes characters start changing in ways you don't expect. Let them, and don't let your brain tell you not to do it; overthinking things is going to be your downfall.
In other words, if you do it, I suggest doing it in a way that changes what you didn't like about it to begin with and go from there. Figure out a plot, stick the characters in there, and just let them play around for a while. Then decide if you have enough to make a full fanfiction off of. Sometimes characters just get too stilted to work with, unfortunately.