If you insist on having the same article, the genus must be feminine - That's the only case where the singular and plural article is the same: die.
If you insist on having the substantive in singular and plural the same, this calls for the so-called "Nullplural" (i.e. singular and plural word is the same, no changes to form the plural). This exists in German, but to my knowledge only for masculine and neutral gender substantives (Maybe for exactly the reason you're asking for).
There are some corner cases with female abbreviations that can carry an article - "die SMS" (German abbreviation for a text message) is an example. IMHO that doesn't pass the "word" criteria you set up, though.
So the general answer is: No (even if non-existance is hard/impossible to prove - But I don't know any)