Is it permissible to pray Jumu'ah while in a state of ritual impurity (janabah) after waking up to sexual desire and an involuntary ejaculation, without conscious will?

You must take the initiative to perform ghusl (ritual bath) from janabah (state of ritual impurity requiring ghusl). If you catch the Jumu'ah (Friday) prayer, perform it; otherwise, perform the Dhuhr (noon) prayer. It is not permissible to pray before performing ghusl, except for an excuse that permits tayammum (dry ablution). The jurists unanimously agree that a person in a state of janabah should not perform tayammum out of fear of missing the Jumu'ah prayer; rather, he should perform ghusl. If he misses it, he should pray Dhuhr.