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Footslogging Chaos sounds like fun, actually.
In theory, you'd want a couple of Troops choices to sit on home objectives. Then some fast-movers to get to grips with the enemy, or at least get to the 24" 'sweet spot' of MEQ armies.
Finally, deepstriking units that can hold out against fire for a couple turns. Lesser Daemons can do that with numbers. Terminators can do that with armor saves.
Then toss in some walkers, either dual-CCW Dreads, or a Defiler. Take a look at a Daemon Prince, or Summoned Greater Daemon, too. All of these can ignore or soak small-arms fire. Having them might alos keep heavy weapons from targeting your smaller guys.

As you said, it's an uphill battle. You likely won't win 'Ard Boyz with it, but can likely score some cool points on the build. Make them masochistic followers of Slaanesh or something. They love the pain!

Being a traditionalist I prefer mono-god Chaos armies. I've been considering a foot slogging Khorne army. I'm not sure how it would do, but here is the concept:

Three 20 figure blocks of Khorne Beserkers (or just plain CSMs with a Khorne icon if I'm short on points) as the core. I'm thinking 20 man units to mazimise their survivability, but six ten man units might work well as they will spread out enemy fire. These are delivery systems for two close combat monster characters: Kharne and a Khorne lord on a juggernaught with a daemon weapon. Two close combat dreadnaughts running along with the infantry mainly to draw fire from the infantry blocks. A big unit of lesser daemons that will used as a screen once they show up. A unit of terminators and perhaps some obliterators to deep strike into the enemy army to cause a turn or two of havoc and once again buy some time for the infantry block to get across the table. Perhaps some havocs and a vindicator to provide ranged fire support. Finally a summoned greater daemon because it's probably one of the best 100 points in the CSM army. With any luck it will show up the turn after the terminators and thus can get in amongst the enemy quickly. Barring that, it's much like the dreads: a threat they simply cannot ignore and thus will draw fire from the infantry.

I have not run the points on this, but it sounds promising at least in theory.

TR

20 man that's not fearless is asking for trouble.
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As for large blocks, it works better at higher points when you can purchase the blocks in addition to the supporting elements.

Large blocks also mean less special weapons and power fists. So you will have to rely on multiple assaults...which is not a reliable thing when the movement is stuck at infantry pace.