Does the Infinite Staircase connect with Sigil?

I'd just like to say I agree completely!

I think here we get to start wondering which has more power to exert its desire: Sigil or the Stairway?

DM's decision. I would decide on them being seperate.

The group of planewalkers I'm DMing for knows a few portals in Sigil and a few portals on the Stairway. Now, one time they were on Arborea and the nearest accessible portal was one to the stairway, their destination was a Prime world to which they know a portal from Sigil. The only plane where they knew portals to both Sigil and the Stairway was Bytopia. Yup, the Portal to the Stairway was on Shurrock, the Portal to Sigil NOT on Dothion, but in the Outlands gate town of Tradegate. So, they had to travel the stairway, Shurrocks wilderness, the connecting mountains, to the town of Yeoman, down the trade road to the Gate to the Outlands, through the wilderness of the Outlands to Tradegate, then to Sigil, then through two wards. Along the way I of course pestered them with monsters, wildlife, weather, NPCs, adventures etc. so this trek became a minicampaign of half a dozen evenings. And we had much fun exploring the planes. Wouldn't have if there were easily accessible shortcuts. IF I ever introduced such a shortcut, it would be at an extremely akward place (monster-infested Undersigil or some such) with a ridiculously hard-to-get key, otherwise, there wouldn't be much walking in 'planewalker'.

The Infinite Staircase connects to Jangling Hiter, which has so little beauty and artistic merit that it was completely unaffected by the Iron Shadow, a plague that drained most of the creativity out of the places it touched, causing the architectural wonder of a formian city to transform into mere dirt tunnels and a major rilmani metropolis, along with all its inhabitants, to turn to piles of salt. The Staircase leads to the city of your heart's desire, whatever your heart's desire is. Even if you don't desire great artistic merit or beauty.

The Infinite Staircase is drawn toward creativity, but Tales From the Infinite Staircase says that even one artistic soul, alone in the wilderness, is enough to attract it. The longing of a person for a place is enough to create a connection, regardless of the nature of the place to which it connects.

Thanks Rip,I can always rely on you!

 I thought the heart's desire thing was a danger of the stair, smething that would come up every once in awhile and attept to lead the character off to permanent NPC land. Don't currently have a copy of the supplement so I'll have to rely on you. 

Not as far as I know. There are lots of infinite things in the planes.

I've been thinking of expanding on the idea of the Infinite Staircase leading to the city of one's heart's desire. Let's say you grew up in a city that has since been flooded and conquered by subterranean mushroom dwellers, and your heart's desire is the city before it was flooded, as you remember it from your childhood. Does the Staircase reach through time? It could. But what if your heart's desire isn't the city as it actually was, but as you remember it, an idealized image without unhappiness or crime? Can the Staircase reach that city? If you reach an idealized image of a city that never was, what happens if you walk outside it? Does the Staircase create an entire world to support the city, or do you just find the unformed mists of the Ethereal Plane, or the void between the staircase flights? Is the city real, or just a hollow image populated by souless automatons? If it wasn't real, it'd hardly be the city of your heart's desire, and the choice to stay or leave it wouldn't be as wrenching.

Perhaps the Infinite Staircase has the power to actually overwrite cities, replacing them with the fantasies of those who have walked it - but only so long as the stairwalkers remain there. If they leave, even for a moment, whether through the Staircase or by ship or land on the plane the city exists on, the city reverts to the way it was, forever, and the stairwalker never finds it again. I suppose it depends on what one's true desire is. Perhaps some people are satisfied with castles in the air, untethered to any world or plane, surrounded only by void or mist. It's probably safe to say that the Lady of Pain has the ability to prevent her city from being overwritten - but she wouldn't have the ability to prevent alternate Sigils from being born in half-worlds connected only to the Infinite Staircase. Those would have nothing to do with her.

Tales From the Infinite Staircase says that the staircase is drawn toward places of creativity, but I wonder if it might not be generated exclusively by the wishes and imaginations of those who walk it, and these just happen to usually be places of art and culture. Perhaps each rung is sustained only so long as the person who discovered the city lives there. During that time, the city can be visited by anyone who walks the stairs, but when the desirer leaves, or dies, the city evaporates, and so does the flight of stairs that once led to it. 

Or perhaps the cities created by the Infinite Staircase are permanent, and those who dream on the stairs slowly create new permanent planes and new worlds complete with histories and memories of having always existed, expanding the multiverse as they go.