No, both because spell-like abilities are not spells, and more importantly because it would be meaningless.
Spell-like abilities do not normally have somatic components. Warlock invocations are special in that they do have “simple” somatic components that are affected by the Arcane Spell Failure of Medium or Heavy armors. There is no indication that weapons interfere with them, however. RAW, it’s not automatic that the rules for spells apply to spell-like abilities (or else the feat would work); if your DM is houseruling that they do, then he should be amenable to houseruling the feat to work.
Moreover, a Spiked Chain would not interfere with spells anyway – you can carry two-handed weapons with one hand, and can remove and add hands to a weapon as a free action. Thus you can let go of the chain with one hand, cast the invocation, and put the hand back in order to attack with it. Similarly, bucklers definitely leave the hand free to use somatic components, and light shields arguably do. The only people who have to worry about somatic components while wielding weapons are those who are dual wielding.
Finally, I want to point out that eldritch glaive in Dragon Magic is a much better alternative to the Spiked Chain. It is cast as a full-round action, and allows you to make as many attacks as you could in a full-attack, each attack being a touch attack that deals eldritch blast damage. Like a regular glaive, the eldritch glaive has reach (but cannot hit adjacent targets). It’s really the best way to make a melee Warlock.
If you don’t have Dragon Magic, I probably still wouldn’t bother with hideous blow. You can only ever use it to make a single attack, which is pretty poor. Focus on invocations for defense/mobility/debuffs; eldritch blast just becomes a (relatively good) back-up ranged weapon for when you cannot use your Spiked Chain.