That is my interpretation, too.
True. and the word "as if" is only used for "wielding a reach weapon". Not "as if wielding a glaive" or "as if you are wielding a two-handed reach weapon" or something.
So I think the pseudo-reach weapon created by Eldritch Glaive does not require two-hands.
Combining those two interpretations, I say one can perform necessary somatic component when he use this invocation, then can use that same hand to "wield" a (non two-hand) pseud reach weapon.
There may be 3 other possible interpretations.
If you can use the same hand for performing somatic component and wielding the pseudo-weapon, but the pseud-weapon is a two-handed weapon, then you need 2 free hands to use Eldritch Glaive.
If you need a free hand all the way during a full action for this invocation but the pseudo-reach weapon is a one-handed weapon, then you need 2 hands to use this invocation. One to perform a somatic component, and another one to wield a one-handed weapon.
If you need a free hand all the way during a full-round action for this invocation and the pseudo-reach weapon is a two-handed weapon, then, you need 3 hands to use this invocation. One to perform it's somatic component and 2 more to wield a two-handed weapon. Thus usual humanoid warlock cannot use this at all.