In the base game there are five achievements that require you to complete a "layer" of the basement without taking damage. Are these necessary to get the "Golden God" and the "Platinum God" achievements?
Platinum God has apparently been modified and you do have to have all no-damage achievements to unlock that achievement now. (See also.)
According to the wiki you have to get all items from the original and wrath of the lamb expansion in order to get the "Platinum God" achievement, so no.
The "golden god" achievement is just for collecting every item in the original game so you don't need them for this either.