Since a warlock's familiar can be a Quasit (which can turn invisible) and a familiar can be used to deliver the warlock's touch spell, it should be able to deliver a touch spell like plane shift1 (when used on unwilling creatures) while invisible.
But does the familiar get advantage on the attack? The wording of the Unseen Attackers section is quite specific about saying “you”, which I interpret as the caster, not the familiar:
When a creature can’t see you, you have advantage on attack rolls against it.
Does the Advantage apply or not?
1) Plane Shift is horrible as an offensive spell. However, this question might be relevant for Multiclassed warlocks.