Nisaa
No, not until Ghusl is performed. Tawaf is treated as equivalent to prayer in the same reasoning that closes tawaf to a woman in hayd or nifas, and Janabah is squarely a state prayer itself is closed to, so the same closure reaches tawaf. Where Janabah differs is not whether tawaf is closed, but how long: Ghusl lifts it immediately, rather than waiting on bleeding that has to stop on its own.
The Qur'an closes prayer to a person in Janabah directly. 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]. Tawaf is carried into that same closure by the hadith of Ibn 'Abbas (Radi'Allahu 'Anhuma): "Tawaf around the House is like Salah, except that Allah has permitted speech during it; whoever speaks during it should say nothing but good." (Narrated by al-Tirmidhi; graded sahih by al-Albani, though al-Nawawi and others held that the correct view is that this is a statement of Ibn 'Abbas himself rather than words of the Prophet). Because tawaf is equivalent to prayer in everything but the permission to speak, and prayer stays closed to Janabah until Ghusl, tawaf is closed on the same terms.
Where the four madhabs differ
This is the same disagreement that separates the schools on tawaf during hayd or nifas, carried over to Janabah on identical reasoning. The Maliki, Shafi'i and Hanbali schools hold that purity from hadath, Janabah included, is a shart, a condition without which the tawaf does not count at all. A tawaf performed while still in Janabah would need to be repeated once Ghusl is made.
The Hanafi school treats purity as wajib rather than a shart for tawaf's validity. On this view a tawaf performed in Janabah is valid but blameworthy, and a dam, traditionally a badanah, a camel or cow, becomes due as expiation, the same concession the school applies when hayd or nifas cannot be waited out.
Why this rarely becomes the multi-day problem hayd or nifas can be
Hayd and nifas close tawaf 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 tawaf that was closed opens again, whether Janabah occurred minutes or hours earlier. A pilgrim who finds herself in Janabah before tawaf, whether from intimacy with her husband or a wet dream during the trip, simply makes Ghusl and proceeds; there is no equivalent to waiting out a period mid-Hajj.
The mosque itself is affected too
Because tawaf takes place inside Masjid al-Haram, a person in Janabah also cannot enter or remain in the mosque to reach the Ka'bah, beyond the narrow exception the same ayah makes for passing straight through. Both restrictions lift at the same moment Ghusl is complete.
This stands apart from tawaf during istihadah, which is not affected at all: istihadah is not classed as a form of major impurity the way Janabah is, so none of the four madhabs treat it as reaching tawaf in the first place.