Man at one point I had 5 of them to solve, I have always moved on to another race when the rare showed up... I just couldnt be annoyed to spend like 150 fragments on creating a useless rare at that moment (instead of solving one for 40 or so and having chance for the rare I want to pop up).
On topic of them having impact on each other.. I doubt it but there are some theories, probably based on nothing. One way or the other I made sure to have 0 rares when burning 1400ish fragments attempting ZinRokh (and I got it ).