Is my utterance of the Two Testimonies valid without having performed ghusl, based on the analogy of one who prayed without ghusl then performed ghusl and did not repeat the prayer, and what is incumbent upon me if it is not?

Ablution (ghusl) is not a prerequisite for converting to Islam. Whoever utters the two testimonies of faith (Shahadatayn), knowing their meaning and being certain of them, has become a Muslim. Scholars have differed on whether the ghusl for conversion to Islam is obligatory or recommended. The preponderant opinion is that it is recommended. Evidence for this is the hadith where the Prophet (peace and blessings be upon him) sent Mu'adh to Yemen, instructing him to call people to the Oneness of Allah, prayer, and zakat, without mentioning ghusl. The ghusl should be performed after uttering the two testimonies of faith.