That's extremely unlikely. Because that means generating a character would come with a LOT of baggage.

That said, if there is a random hash per player that is then parsed somehow, then there would be some amount of pre-deterministic nature to it. But given all the different RNG elements, we would be looking at a large number of uniquely different de-hashing method. Mere offsets won't do because then there would be very observable patterns.

So while possible, it is hardly feasible from a programming standpoint. Not that it's extremely difficult, but there just aren't justification for spending hundreds if not more man hour on something like this. Contrary to what you might think, not everyone is out to get you.

On another note, according to the coupon collector's problem, the number of rare you need to get before getting all the rares, on average, is 21.74. Now, it seems that the first 3 or so are guaranteed non-repeats, but even with that it's still 21.26, which hardly makes a difference (since it is the last ones that have the biggest weight. The last two takes, on average, 4 and 8 respectively)

Considering the average of ~60 pull per rare, that puts you at around 1200 pull or so, in other words, the time at which you get the full collection is roughly the time when you get the super rare. So no, missing one or two is not a conspiracy, it's a normality.