The Ritvah in Kiddushin 38a says that one cannot fulfill his obligation of eating matzah by eating mon, since it does not consist of the five grains. Rabbenu Gershom in Menachos 45b says that Klal Yisrael could not bring a korban Omer or Shtei Halechem in the midbar because these korbanos must be brought from foods that consist of the five grains.
The Nodeh B’Yehudah (Orach Chaim Kama 38) says that there was no obligation to take off challah from mon because it did not consist of the five grains. If the mon would have transformed into the actual food, he writes that it would have been obligated in removing challa.
The Ragatchaver Gaon, in his sefer Tzafnas Paneiach (siman 3), discusses whether a food would become a prohibited food if someone desired to eat that forbidden food, for example if one desired to eat pig, would the mon become a pig? He cites a Gemara in Sanhedrin 59b that says that something that falls from heaven does not become prohibited.
We can assume that whether one could fulfill the mitzvah of matzah or bring certain korbanos and if the food is obligated in giving challa, is dependent on whether the mon underwent a physical change or not. If it did then one would be able to fulfill these obligations. However the question of whether the mon would become a forbidden food would apply even according to the opinion that the mon only assumed a new taste. This is because regarding issurim if something has the flavor of a forbidden food, it too becomes forbidden.