Nisaa
No. A person in Janabah does not pray, whether the prayer is obligatory or voluntary, until Ghusl is performed. This is one of the plainest points of agreement across the four madhabs; none of them holds otherwise.
The ruling comes directly from the Qur'an. Allah says (interpretation of the meaning): “O you who believe, do not approach prayer while you are intoxicated until you know what you are saying, nor while in a state of Janabah, except as one passing through, until you have washed.” [An-Nisa' 4:43]. The ayah names Janabah by name and pairs it with prayer specifically: approach is closed until Ghusl, with a narrow exception for someone merely passing through rather than praying. Where water genuinely cannot be found, whether from illness, travel, or its absence, the same ayah permits Tayammum, dry purification with clean earth, so that prayer is never simply abandoned.
Unlike Hayd, it lifts the moment Ghusl is complete
This is what sets Janabah apart from prayer during Hayd and Nifas, where prayer stays closed for as long as the bleeding itself continues, regardless of anything she does in the meantime. Janabah carries no such waiting period. The moment Ghusl is performed, the prayer that was closed opens again, whether that is minutes or hours after Janabah occurred. What is suspended is only the next prayer, and only until Ghusl restores purity.
Not the same routine as Istihadah
A woman with Istihadah prays as normal, taking Wudu and a protective pad before each prayer, without repeating Ghusl. Janabah asks for the opposite: Wudu alone does not lift it. The full Ghusl set out in what causes Janabah and when Ghusl becomes obligatory is required before salah can be prayed, however recently the last Ghusl was made.
What else the same state affects, and what does not
The mosque is closed to a person in Janabah in the same way prayer is, apart from the narrow exception this ayah makes for passing straight through; see entering or staying in a mosque during Janabah for how the four madhabs read that exception. Fasting stands entirely apart from all of this: a fast remains valid even if Janabah is still present at Fajr, because it was never conditioned on purification from Janabah the way prayer is.