There is one pet called Bugsy Capone who does damage sometimes. It is obtained from buying the Vular Lady pack.
The others have no stat buff, nor effect.

The pet bought from the hive does add stats. "Baby Vular Queen" adds 5 H/s and 5 M/s (these are hitpoint and mana regen)

Some vanities from special event have special effect.
Exemple: mom bouquet, frostmark wing, ... more