The ball of pet summoning is a mysterious tool that works everywhere you don't really need it. So, of course, it doesn't work in abyss.
You can walk down with the dragon, it is just very boring because of the very advanced path-finding algorithms of the pet: it will get stuck at every step, he will block, stop responding, then it will be ganged and you'll have to kill all the spiders to "release" it... horrible experience, really.
The most used strategy is to get the dragon out of stables, park it somewhere, walk your way until the navrey lair, hide and relog: the pet will then appear near you.
Imho is an exploit because the autostable feature was meant to overcome some of the effects of the many bugs that influence pet's usage, not as a pet of ball summoning that actually works.
Anyway Navrey's lair is a relatively safe place so the chances to be revealed in the few seconds required to get your dragon are very low.