I assume it's a mixed marriage with the WNA on KITAS/P?
Officially the impact could be huge since the paperwork (KITAP/KTP/KK) should always correspond with the address where someone resides.
However, I don't know any country as RI where it is such a national sport to have the KTP still reflect a former address. Of course the WNA's position is more risky (dealing with Immigration) but as long as it's a trial and it is not communicated to everyone, I don't think it will be an issue.
Of course a permanent move and esp. a divorce changes everything.