Based on the fact that armor/weapons are graded by quality and effect how well they do in combat I'd guess we'd see the same here plus i doubt blizzard would add a stat like this if it was just for show and no one can even see it
(at least not on the current beta as there's no way to link it or anything). assuming that's the case here are my thoughts on the fixed rarity values for each type of pet.
IMO all dropped pets should be based on their drop rate/current quality, green wing mccaw should be poor, hyacinth macaw should be epic, disgusting oozeling should be epic, deviate hatchling should be uncommon and gundrak hatchling should be rare.
1-100 = poor
101-500 = uncommon
501-1000 = rare
1001-5000 = Epic
5001+ = legendary
Vendor pets should keep their current quality so the cats from elwynn forest are poor, argent tournament pets are rare etc.
Blizzard store pets:
This one is tricky to come up with a rarity value for, if it's poor-uncommon then people feel ripped off but if it's epic-legendary then it feels like a pay-to-win store. Perhaps make them rare in quality but then you'll never have a epic-legendary boss pet...
same as above, hard to figure out how any fixed rarity would fit in.
Special promotion pets:
These should be legendary but then it's unfair to the people who couldn't obtain them, I'm also unsure how these pets would work with a fixed rarity value.
In conclusion I don't see how the rarity value system can work if it ends up effecting combat.