As a non combat option outside of battlefields I think all the races could have a pet of some sort: Space Marine: Servo Skull Cherub Chaos SM: Daemon Familiar Ork: Squig Snotling Eldar: Gyrinx Juvenal Dragon (Think Baby Raptor)
Space Marines also have human servants, usually people that can't complete the SM training but manages to survive http://wh40k.lexicanum.com/wiki/Chapter_Serf#.Ux8b4fl5Oao . I think it may be kind of cool to have a serf in your room cleaning your power armour.
space marines also have servitors chaos also have cultists (if IG arent included as 2 factions--loyalist and chaos) chaos also have servitors/servo skulls/corrupted cherubs but yea, good list
The reason I didn't list every possible pet is my list could be small creature pets that could follow you around as a non combat item, while yes some servitors are children sized most are humans who have in some way failed the Emporium in some way and have either been sentenced to so many years service as a Servitor or something like someone dying early but the body still used to serve. Something that big would be a bad sort of pet in my mind so its one of the reasons I did not list them.
Don't get me wrong though I guess mini versions of chaos cultist or servitors could be a thing I just think its getting a little too close to WoW pets at that point and is something that people might frown on.
The only "pets" that do not go against the fluff are servitors for techpriests/inquisitors and squigs for orks. It's not even certain that techpriests will be in the game, as far as I know. Adding pets because other MMO's have it is not a good idea.
The Eldar Gyrinx would not be lore breaking nor would dragons seeing as they are both in the Eldar lore and way of life.
Just curious, ive never seen any artwork of Eldar and any kind of a reptilian beast, care to post a pic or two (well ive seen it in Fantasy with the Dark Elves)?