you know with Convergent evolution, all the human-like species are actually pretty likely.
I don't see the Hanar and Elcor races/nations having a bigger role due to their smaller military size and such, but i can see a single one or group of them have a bigger role in the story like Saren or Cerberus(pre-ME3). It would be the Leviathans or Rachni who could have a more prominent role on the bigger stage like the Collectors or Geth.
It is the gameplay where they are would be hard to do as a companion, a Elcor would be slow so how would they be able to outrun the many explosions that tend to happen and they would have to use a completely weapon and power system then every else. The Hanar would be a nightmare to do, i'm not sure where i would begin with them.
That said, they could easily work in a non-combat role like Joker, for example a Hanar doctor.
I agree that the Hanar, Elcor and Volus races; as of the current setting; don't have the military strength or capability to match races like the Turians or Humans, but if the upcoming game is set in the aftermath of the Reaper war, then those 'lesser' species who were ignored for the most part; at least compared to the major Council races; could start to fill in the gaps left by the decimated Turian and Human forces. Not that I want to see an emerging Elcor empire as the focus for the next Mass Effect mind you.
The biggest thing I want when it concerns those three races, is characters with more screen time, bigger, more important roles, and most of all for them to lose (or at least distance themselves) from the "Jester/Funny/Comedic Race" moniker that currently hangs over them. More characters of Barla Von caliber and very, very, very few characters of the Blasto theme.
The Leviathans are an interesting topic for future titles, they are definitely suited for a 'behind the scenes' type role, however I am not sure how willing BioWare will be in having them as big players considering how closely they are associated with the Catalyst, and the fact that they are essentially organic Reapers.
Now the Rachni are actually my favorite alien species of the setting so I hope to see them in a larger, more prominent role in future games. They are the most 'alien' alien so I am interested to see how they will interact with the other races of the galaxy, and I would like to see more of their unique insect-like culture and ideology explored further. Your Geth comparison is appropriate, though I hope that the Rachni will avoid 'pulling a Geth', like how the robotic race did in ME 3's Rannoch arc. Nothing would be more annoying then for the Rachni to slip into the Pinocchio troupe and lose what makes them unique.
Gameplay-wise I agree that playable/companion Elcor or Rachni characters will be difficult to do, but not impossible. Humanoid animations are rather 'standard' for the games; Garrus and Kaiden used the same animations for walking, running, etc; I don't see why a non-human animation, and gameplay mechanic can't be implemented. I mean BioWare said that the benefit of using the Frostbite 3 engine was that everything was interchangeable with other Frostbite powered games, and that it would eliminate having to recreate assets. If BioWare can save time and effort in creating their games, then why can't they use some saved time to work in non-humanoid animations and mechanics?
Lore-wise, just because we only see the Elcor walk doesn't mean that they are incapable of running, or maintaining short bursts of speed, and the Rachni have been shown to take out armored columns with nothing but their claws and acid spit. I mean we can accept Shepard being brought back from the dead, but an Elcor or Rachni soldier is too much?