It's certainly possible to see if a Pokemon has their Hidden Ability in an SOS chain - a lot easier than finding a Hidden Ability mon in a horde.
You can force them to show their ability: enter an SOS chain using a Pokemon with the ability Trace, or with the move Skill Swap, Role Play, Entrainment, Simple Beam or Worry Seed. This ability and these moves will reveal the opposing Pokemon's ability on the screen, thus indicating whether it has its Hidden Ability or not. These moves only show the ability for a small moment, so if you miss it, you won't really be able to see it again. Furthermore, Trace copies the ability of a random opponent and is only usable once.
If you have a small attention span (like me), you can try let them present their ability themselves by attempting to trigger the opposing Pokemon's ability. This method varies hugely in difficulty. For example, find a Pikachu in an SOS battle and use an Electric-type move. If it gets hurt, it has Static, its regular ability. If it endures no damage and raises its Sp. Atk, it has Lightningrod, its Hidden Ability. Easy! Unfortunately, many Pokemon do not have as obvious abilities, but there are still ways to work around that, such as exploiting the Pokemon's regular ability. E.g. Caterpie has Shield Dust as its regular ability and Run Away as its HA. There's no good way to indicate a Pokemon's Run Away ability, so you have to look for Shield Dust. To do that, you'd have to use a move with a secondary effect and see if the secondary effect takes effect. If there's no secondary effect, it has Shield Dust. If there is, it has Run Away. Most SOS Pokemon (and horde Pokemon, back in the day) have a way to get their ability exploited, so I hope your desired Pokemon is easy to exploit.
Hope I helped. :)
Source, Source and the example Pokemon's respective Serebii pages