No.
It specifically mentions that warlock eldritch blasts and invocations are subject to arcane spell failure because unlike most spell-like abilities they have somatic and/or verbal components, albeit simple ones that can be cast while wearing light armor (or medium with Battle Caster feat).
So in that situation, no they couldn't. And since spell-like abilities are in all other circumstances non-somatic/verbal, there's no Still/Silent Spell-Like Ability feat (unlike Empower/Quicken/Maximize). So you'll never be capable of casting them in that situation.
From Complete Arcane, page 7:
All invocations, including eldritch blast, have a somatic component.
[...]
Unlike other spell-like abilities, invocations are subject to arcane spell failure chance.
I was thinking about this too, so here's my build (added an additional Feat from your houserules):
Lvl 4 Tiefling, Archfey Tome Warlock
This build points to forgive the melee and AC options for a more focused caster. I liked your idea of an hybrid, but seems to me that it really needs to be an hexblade, going in the direction of the other classical builds around. Tiefling adds some interesting features, while allowing to reach 20 CHA on lvl 4, increasing the overall effectiveness and chance to hit of the few spells you can cast.
By Lvl 4 you have:
- Cantrips: Eldritch Blast, Minor Illusion, Vicious Mockery, Thorn Whip, Shocking Grasp, Thaumaturgy, Friends
- Lvl 1 Spells: Hex, Sleep, Faerie Fire
- Lvl 2 Spells: Hold Person, Phantasmal Force
- Hellish Rebuke 1\day (2d10)
- Fire Resistance
- Agonizing and Repelling Blast
I chose Archfey over Old One for several reasons:
- Spells: Dissonant Whispers and Tasha's seems kinda redundant to me, especially when you can get Hold Person at lvl 4. Sleep it's an
excellent spell vs. low level mass enemies, it has no concentration
and grows with spell slots. Faerie Fire can grant advantage to the
entire party vs one or more hard targets. Both pacts have Phantasmal
Force which is a great disable for low int enemies and fun to use too.
- Pact Powers: Fey Presence is an area disable which fits more the theme than Telepathy granted by Old One. At lvl6 Entropic ward is
fine, but Misty Escape is simply awesome.
Invocations: I'd go to PimpMyBlast just because this is your only reliable source of damage in a lot of situations where CC or forced movement are not options - If all CCs fails, if you want to blast that minion in the backrows not worthy a spell, in long fights, ecc..
But if you like, you can forgo one of the blast invocations to get rituals, which can give you a bit more flexibility and a Familiar.
Feats: i'd really like going first at all costs with this build, so i'll take Alert. A well placed Sleep or Hold person the first round is no joke. Otherwise Moderately Armored can give you better ac with a shield, but going melee will require War Caster too to be a viable option.
Ability scores in order of importance: Max Cha, High Dex, High Con, Mid Wis, Low Int, Low Str
Role: cc\secondary caster
Playstyle: Disable high treat enemies as soon as you can. Use forced movement (Blast, Thorn Whip) to generate AO from allies and reposition enemies at your vantage. Minor Illusion to modify battlefield (covers, false gaps, ecc), Vicious Mockery to help ally, Shocking Grasp to disengage, Thaumaturgy\Friends as social tool.
Progression: At lvl5 you can get the infamous Devil's Sight + Darkness combo which can transform you into a walking nightmare of disabling madness, very hard to target. Lots of tactics here, disabling sight with plain movement is a powerful option, plus you attack with advantage; just take care of LOS of your allies. If you want more utility you can always get Rituals. Darkness is 1/day from Tiefling so you can also get a lvl 3 spell. While patron's spells are not that great, at lvl 3 you have 2 strong area disables (Fear and Hypnotic Pattern) and Counterspell, which is really useful if you are the only caster in the party.
Here is Lvl detailed progression:
lvl 1
Tiefling: +2 Cha, +1 Int, Thaumaturgy
Patron Fey: 1-turn Area disable
Spells: 0 - Eldritch Blast, Minor Illusion; 1 - Hex, Sleep
lvl 2
Invocations: Agonizing + Repelling
Spells: 1 - Faerie Fire
lvl 3
Pact of the Tome: Vicious Mockery, Thorn Whip, Shocking Grasp
Spells: 2 - Phantasmal Force
Tiefling: Hellish Rebuke 1/day
lvl 4
Spells: 0 - Friends; 2 - Hold Person
Feats: Alert (from houserule 4th lvl)
Best Answer
You are absolutely right, an Eldritch Blaster is usually stronger
After the 2nd level, when you get Agonizing Blast you can do d10+Cha damage, which is the same average damage as using a longsword two-handed if you are Strength primary. You can attack twice with both at level 5.
At level 11 Eldritch Blast pulls ahead with 3 attacks, and the Charisma bonus on the Pact Weapon damage on next level (Lifedrinker invocation) can not compensate for this, unless you take the Polearm Master feat. Add to this that a Blaster only needs Charisma, while with a Pact Blade you need Strength if you want to do good damage and Charisma for the spells.
Xanathar's Guide To Everything
This book provides many new and powerful options, particularly the Hexblade Patron and Eldritch Smite and Improved Pact Weapon invocations.
With these, you can outshine a Eldritch Blaster quite often, and a Ranger any time.
However, I think you look at it all wrong
A melee Warlock is on par with a Ranger on most levels, somewhat smaller base damage and HP, same number of attacks, same AC, but better versatility. This shows it is viable as a build.
The Eldritch Blast is just a bonus. Not using it is indeed self-nerfing, but only in a way that playing a Ranger instead of a Fighter is self-nerfing.