Looking at the text of Eladamri, Korvecdal and Agatha's Soul Cauldron I'm inclined to agree that without Eladamri, Korvecdal in play you should not be able to see the top of your library if you activate his ability that has been granted to another creature through Agatha's Soul Cauldron. I say this because it is Eladamri, Korvecdal's passive ability that give you permission to look at the top card of your deck, and without him being in play to give you that permission his ability should be a blind flip if you choose not to reveal from hand.
Eladamri, Korvecdal
{1}{G}{G}
Legendary Creature — Elf Warrior
You may look at the top card of your library any time.
You may cast creature spells from the top of your library.
{G}, {T}, Tap two untapped creatures you control: Reveal a card from your hand or the top card of your library. If you reveal a creature card this way, put it onto the battlefield. Activate only during your turn.
3/3
Agatha's Soul Cauldron
{2}
Legendary Artifact
You may spend mana as though it were mana of any color to activate abilities of creatures you control.
Creatures you control with +1/+1 counters on them have all activated abilities of all creature cards exiled with Agatha’s Soul Cauldron.
{T}: Exile target card from a graveyard. When a creature card is exiled this way, put a +1/+1 counter on target creature you control.