Knowing both English and Japanese it's fascinating to see what Japanese words the English speaking world finds interesting. All sources seem to point back to the 2014 article by Jonathan Crow.
In essence I see this as the equivalent of "backlog" in most cases, i.e. (my backlog) is piling up. And is otherwise a fairly straight forward concept to convey in English. Hardly "untranslatable", and seems rather silly to import a word that's more or less a pun that would be lost upon all of the people using it.
One thing the English wikipedia doesn't mention is that 積んでおく (tsundeoku) has a contraction/slang form 積んどく (tsundoku) which I think solidifies the play on words to create 積読.