By default, handleLeashedCreatures is true.

Having said that, when trying to traverse between two A networked gates 5 chunks apart, the leashed animal fails to teleport.

Looks like any entity (including non-mobs and players) can be the start of a chain, but only mobs can link to it.
Only mobs can link to a mob attached to the origin entity, but this can be repeated infinitely.

The origin entity (as it can be a non-mob) can be a stack of mobs.
Follower entities can not be stacked -- they need to be singular mobs.
If a stacked mob is attached to the chain, the passenger entity will dismount.

As such, there are realistically two possible edge cases concerning leash handling:

1. A player (and the player's passengers) enters a stargate while leashed to a mob (which may be leashed to any number of mobs recursively).
2. A minecart (and that minecart's passengers) enters a stargate while leashed to a mob (which may be leashed to any number of mobs recursively).

Looks like players are exempt from the above restrictions.
i.e. players can ride connected entities, even though mobs can not.