First I'd like to start with the most basic question: is it even viable to run these guys without any vehicles. Neither their armour nor their move-and-fire weapons support being on the ground. They're not tough and the assault models don't have grenades. Compounding that problem, there is the issue of numbers. Even with Coateaz we can't take them en masse like the IG can do with platoons. So with 6 troops slots and points being as they are, throwing away units on speed bumps isn't an option.
Despite these problems, I think the answer is still yes. It's just that certain squad compositions support foot lists better than others. Let me lay out a few I have in mind. Some are obvious, net-established units but please bear with me as I'll make a case for their use in foot lists, something that I think is not obvious.
The 80pt Deathray
-8 Psykers. That's it. We're just paying for 8 bodies with one gun, but what a gun! They have quite good range and the best S and AP you can get, with a large blast too. I think they work in foot lists because of their range and versatile LOS. They can fire from any model so you can easily hide the bulk of the unit with one or two guys getting LOS. This also allows them to get multiple angles.
Guns, guns and...oh right, GUNS!
3 Servitors (user's choice of Multi-Melta or Plasma Cannon) and two Jokaero to start. From here I see a couple variations. 7 Psykers makes for a potent and versatile shooting unit. If you attach Coteaz 3 melta or plasma Acolytes may be a good way to take advantage of the I've Been Expecting You because the range matches up well. And going that route 1-2 DCAs and 1-2 Crusaders may give some guys to take saves with and some others to provide a little CC defense at great initiative. They work in foot lists because of the sheer fire power involved. No matter how you equip them, their guns are frightening. Coteaz is an awesome addition for the aforementioned reason, but an Ordo Hereticus Inquisitor with Psyocculum should be considered as well as any unit even containing a single psyker can be shot at max BS, hitting on 2s and rerolling for 2s. Plasma Cannons and the Psyker Blast will deviate a maximum 2 inches. It's kind of ironic how broken this is against Grey Knights.
Detachable pe...er Melta!
3 Melta Acolytes. Yup a free kill point. But if you don't mind that and you're facing an IG parking lot, maybe it wouldn't be so bad to use a Grand Master to make them outflank. If they're too disposable for your liking, add more Acolytes and use them behind GKTs and PAGKs. They're still cheap that way and can get a cover save.
I see you've played knifey spooney before!
A mix of DCAs and Crusaders. I think the key to using these guys on the ground is going heavy on Crusaders for their saves. I also like a Banisher (with Eviscerator if points allow) and a Mystic if you run with GKs that can DS in to support you. You now have a unit that has pretty solid defense, little need for cover, support potential, and incredible CC ability. They lack grenades, so that limits them to counter assaults and charging units that come out of transports. Might be better to take GK units to assault with, but this is how I've felt about these guys.
Those are the four (with some variations included) that I'm consistently drawn to when list-building. I'd really like to use Daemonhosts but I haven't tried to make them work because the task seems so daunting with their random abilities.
I don't really see any lists posted for Inquisition without vehicles. Maybe that's because it just doesn't work against tough lists. If that's the case, post up and let me know
I'd love to hear what others' experiences are like. If possible let me see lists you've had success with, or that you think might work. I'll post two of mine sometime soon.