Is the fulfillment of a vow considered valid if the Fajr prayer was missed on its due time during continuous days of fasting that were vowed, with the missed day being compensated for by an additional day?

Conditional vows are disliked, but fulfilling them is obligatory. Vowing to pray Fajr on time is not binding, because Fajr prayer is already obligatory, and there is no vow for something already obligatory according to the majority of jurists. Your failure to observe this vow is a failure to observe what is obligated by the Sharia (definition), not by the vow. Since you completed the fast on the day you vowed and did not change your intention, you have fulfilled your vow.