Getting back to the point, I probably wouldn't allow a paracritter as a pet - mainly because few paracritters are domesticated.
If the character had a decent backstory (or somehow managed to do it in-game) and had a high enough Animal Husbandry skill (5+ or so, at least), then I might consider it. Mostly it would be a roleplaying thing, though, as few runners regularly have people over to their house.
As a roleplaying thing, there would be lots of aspects to consider: what does it eat? How often does it need to be walked? What does it do when the runner is not around? What arrangements does the runner have in place if they need to go to hospital for an extended period?
If both you and your player are willing to put the effort in, then by all means do. I suspect the player may find it more trouble than it's worth, but that's the wonderful thing about roleplaying.