Do it!
Well, since readers aren't your goal, I won't talk very much about them, but some can read one of your stories and get interested in the other when otherwise they'd never look at it for some reason.
Now, while I suffer from a case of dropping stories because of time, I recommend you start a second one if that's something you're interested in.
In my experience, working on more than one story can give you the distance to look at the chapters in a new light. When I'm writing one chapter after another for the same story, I can get caught up in the pace and not notice things.
I have this image in my mind of what I'm doing and, if I don't pay attention or get too caught up in the writing, I may not notice that my vision of what I'm writing may not match the impression my readers are getting.
If I take a day to work on another story, and then get back to the chapter, I usually notice things I had missed, or the idea I wanted to portray in the chapter crystalizes, improving the experience.
On the other hand, yeah, you won't have as much time to work on the original fic you were writing.
Really, if you write mostly for yourself, I recommend you ask the question, DOES THIS NEW STORY INTEREST ME? WILL I REGRET NOT WRITING IT?
If it's just a whim, try to write a small chapter for fun, without much thought and get it out of your system, but if it's something you really like, don't let it go without at least trying.