Nisaa
Yes. Janabah does not invalidate a fast, even when it is still present after Fajr and carries into the fasting day itself. This is one of the clearest places fiqh draws a line between a state that stops worship outright and a state that only requires purification before the next prayer.
The evidence is direct. 'Aishah and Umm Salamah (Radi'Allahu Anhuma) both reported that the Prophet (Salla Allahu 'Alayhi Wa Sallam) would enter the morning in Janabah from intercourse with his wives, not from a dream, during Ramadan, and would then fast that day. (Narrated by al-Bukhari and Muslim). This is not an isolated exception; it describes his ordinary practice.
There was an early difference of opinion on this point, and it is worth knowing because of how it was settled rather than argued away. A report attributed to Abu Hurayrah (Radi'Allahu Anhu) held that a person who reaches Fajr still in Janabah must abandon that day's fast. When Marwan ibn al-Hakam sent someone to ask 'Aishah and Umm Salamah directly whether this was correct, they told him it was not, and that the report Abu Hurayrah had been passing on was actually the words of al-Fadl ibn 'Abbas, not the Prophet's own practice. On hearing that, Abu Hurayrah accepted the correction. The four madhabs today are unanimous on the result: fasting remains valid when Janabah persists past Fajr, provided its cause, marital intercourse or the release of Maniy, happened before Fajr rather than during the fasting hours themselves.
Janabah and fasting are not tied to the same condition. Ghusl is required before Salah, not before the fast can begin or continue. In practice this means she can eat suhoor, form her intention to fast, and delay Ghusl until any time before Fajr salah is due, even past Fajr itself, without the fast being affected at all. Delaying Ghusl well past sunrise is disliked, since prayer should not be pushed back without reason, but the delay on its own does not undo the fast.
This is a genuinely different rule from hayd and nifas, and the difference is worth being clear about. If a period begins during a fast in Ramadan, that day's fast is invalidated the moment bleeding starts, however late in the day, and the day is made up afterward. Nifas after childbirth is treated the same way: the bleeding itself stops the fast for as long as it lasts. Janabah works the other way around. It can be present at the very start of the fasting day and simply resolved with Ghusl afterward, because unlike hayd and nifas it was never an obstacle to fasting in the first place, only to Salah and to a small number of other acts.