Part of me says no, the Lady forbids this entryway because it doesn't utilize portals. Now if a pact binder is already being ridden by a vestige then they can enter Sigil, but the actually summoning doesn't work.
Part of me says most of the time, the Lady would allow it. Though perhaps a vestige like Tenebrous isn't allowed into Sigil, just in case Orcus finds a way to recapture the lost divinity he possessed (mind you, this idea that Orcus isn't divine is a weird shift from Planescape to 3.5e).
I do think there should be something off about vestiges in Sigil, but that's based around the theory that the Lady herself is a vestige able to act to an extent on the physical plane.
Reason I was thinking this was my thoughts on the Lady as Vestige:
""Soaked into me deeper than any lover Ipos whispers secrets in the braids of my muscle and the marrow-filling of my too brittle bones. He tells me the Lady is a vestige that has departed from their place outside the boundaries of true existence. She is a fully present spirit who has no need of a vessel to be Here, to be extant in the Now.
Sigil is Her circle She has summoned Herself into, the circumference-price for Her ability to traverse the axes of the Real.
Can She be killed? Yes, everything can die, but She can only be killed by someone who follows Her, who shadows the Road She took..."
-Praetor Noriia, Legends of the Pact Binders
Vestiges are beings who are trapped beyond life and death, existing a spiritual state quite different not only from undeath but from the rest of existence all together. Normally, vestiges are beyond the reach of the gods but also, to those with the knowledge, able to be summoned by mere mortals known as pact binders.
Summoning a vestige requires a seal, a portal through which it can step trough. In the normal course of this highly abnormal magic, vestiges can only influence reality through those pact binders who take them into their flesh for a time. Even then their ability to work their will is limited both in time and control.
But what if a vestige was summoned, or summoned itself, utilizing Sigil as a seal? A pact to itself, just as it is said that Odin hung from Yggdrasil as a sacrifice to his own divinity? Or perhaps someone else, possibly the dabus, called her here to serve as the city's eternal guardian? Could such a being remain somehow aloof from the powers of the gods but also possess, within that limited circumference, mastery of its environment? After all, their nature is held to be undefinable by the known laws of the Multiverse, and the Lady and Sigil certainly qualify on that front. Not only would it bring meaning to using the Cage to describe the city, it might explain why the city is referred to as a Sigil if it were the Lady's own pact binding seal?
Could the Lady of Pain be a vestige...
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