It really depends on several factors. I was missing some documents for my marriage and the KUA office said they would hold onto my Buku Nikah until I gave them the documents, but after my ceremony they gave me the books anyway signed and stamped. If you've being giving your buku nikah, or your marriage certificate if it was a civil ceremony, then I believe you're recognized as being legally married in Indonesia. As for your home country, mine will issue a letter of non-impediment as a courtesy, but they don't require one for marriage and as long as you have a valid marriage certificate from Indonesia they will recognize the marriage. Your home country may be different.