Are those Gentiles committed to following The Seven Law Of Noah bound to offer burnt offerings?

Shalom, Thank you for your question. When the Temple is standing, and offerings are given there, there is no obligation for a non-Jew to have to bring any offerings. However, if they choose to then a gentile, even an idol-worshipper, could volunteer a sacrifice to be offered at the Temple (Menachot 73b). The only sacrifice accepted from him was a burnt-offering (Olah); Jews, on the other hand, whether they were men or women or converts to Judaism could volunteer any kind of sacrifice (Hilchot Maaseh Hakorbanot 3,2). (Based on a previous answer on our website by Rabbi Blass). Blessings.