Nisaa
Yes, in the sense that Sa'i itself is not held to the same purity requirement as tawaf. What actually delays most menstruating women's Sa'i is not any condition of Sa'i's own, but the fact that it is meant to follow a valid tawaf, and hayd is what puts that tawaf on hold.
The hadith behind nearly every Hajj and Umrah ruling for a menstruating woman is the Prophet's (Salla Allahu 'Alayhi Wa Sallam) instruction to 'Aishah (Radi'Allahu Anha) after her period began while she was in ihram for 'Umrah during Hajjat al-Wada' (the Farewell Pilgrimage): "Do everything that the pilgrims do, except do not perform Tawaf around the House until you are pure." (Narrated by al-Bukhari and Muslim). Sa'i is one of the things pilgrims do that he did not exclude by name. Only tawaf was set aside.
Why tawaf, not Sa'i, is tied to purity
Tawaf's own link to purity comes from a separate 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 it to be a statement of Ibn 'Abbas himself rather than words of the Prophet). Because tawaf is treated as equivalent to salah, and salah requires purity, so does tawaf on this reading. No comparable hadith equates Sa'i with salah, which is why scholars do not make purity from hayd a condition for Sa'i's own validity the way they do for tawaf.
Why her Sa'i still waits its turn
Even so, Sa'i is not performed as a standalone act. Scholars hold that it must follow a valid tawaf, in keeping with the order the Prophet (Salla Allahu 'Alayhi Wa Sallam) kept in his own Hajj and his instruction: "Take your rites of Hajj from me." (Narrated by Muslim, in Jabir ibn 'Abdillah's account of the Farewell Pilgrimage). Since her tawaf does not count while she is bleeding, a Sa'i performed ahead of it would still need to be repeated once a valid tawaf has been made. That is why the answer to what if your period starts during Hajj treats Tawaf al-Ifadah and Sa'i as waiting together, and why what if your period starts during Umrah links the same two steps in the same order: not because Sa'i shares tawaf's purity requirement, but because it is sequenced right after it.
What continues as normal while she waits
Everything else the hadith of 'Aishah leaves open still applies during that wait: du'a, dhikr, talbiyah, reciting Qur'an, and the rest of the acts of worship that stay open during hayd. What does not continue is entering the Masjid al-Haram itself to begin either rite, for the same reason a menstruating woman does not enter any mosque while bleeding.
Because Tawaf al-Ifadah is where the four madhabs genuinely differ, particularly for a pilgrim whose flight home cannot wait for her purity, and Sa'i simply follows whatever is decided about that tawaf, this is worth raising with a scholar together with her exact travel dates rather than settling Sa'i as a question on its own.