It looks like The Golden Monkey is bugged.
Some people have reported that it will not change all the cards put into your deck, others have claim that it will.
Sources for "Does not change added cards":
Sources for "Changes added cards":
- This Youtube video showing a custom match between two friends, the warrior uses the Juggernaut but the priest decks out and never draws a mine.
- A collection of images showing a match against Archaedas, in which the AI uses the golden monkey, but never takes 10 damage after, thus he had never drawn the Burrowing Mine
From the people that have said it does not change, I have not seen actual visual proof,
but there is visible proof of people showing it does change added cards.
This leads me to believe that the answer to your question "Does the Golden Monkey change ALL cards put into your deck?" is
Yes, the Golden Monkey changes ALL cards in your deck, including cards placed there due to an effect. However there also seems to currently be a bug where it may exclude cards added by an effect.