First of all the term “concordat nation” merely means that there is an agreement similar to a treaty between the nation and the Holy See in which they recognize each other’s sovereignty and agree on certain legal and diplomatic matters. A concordat is essentially a treaty, but the word is usually reserved to a treaty between the Holy See and a secular government.
Each relationship is unique to that particular country.
Even the term “concordat nation” is not strictly defined.
So if one wants to know how ANY given country acts with regard to Catholic declarations of nullity, and vice versa, one would necessarily need to review the laws of that country and the concordat(s) which exist. There is no one-size-fits-all answer to this.
I keep coming back to the “no hope of reconciliation” part of your question. You decided to make it the title of your thread, so that seems important.
Do you actually know what Church Law has to say with regard to requiring no hope of reconciliation until considering a petition for declaration of nullity?
Do you KNOW what the law says, or are you just guessing what the law might say?