Link To The Fire
It would have the same effect as when Gwyn linked the fire, which seems it is slowly going out and need a being with enormous power to sacrifice themselves. So yes, your character is manipulated into linking the fire which kills himself. Does it also break the curse of the undead? Maybe, we don't know. All we know is the dark lord ending certainly doesn't.
But here is an important distinction. We don't know if the age of fire continuing empowers the gods. Heck, you can have killed most of the important gods by the time you link the flame. So we really don't know to what effect linking the Flame has upon lordran. What we are told is that it ends the curse of the undead, but we don't know if it does. We also know Gwyn did it at one point, but that seems to be to counter the chaos flame, and made his faithful knights into an elite demon fighting force. And lastly we know Fraampt wants you to do it.
Gwyndolin
It has become a common theme in the community that gwyndolin is the mastermind behind the chosen undead story. The main reason being that his illusion of Gwynevere gives the player the lord vessel. And secondly because he keeps anor londo bright, which has been interpreted as him trying to make it seem like the Age of Fire is still going on.
There are a few problems with this.
If Gwyndolin is the one keeping Anor Londo light and making the Gwynevere illusion, then why if you kill him neither of these are effected? Certainly he aggros if you kill the Gwynevere illusion, but if the other way around nothing happens.
Furthermore why is everyone convinced the Gwynevere we see is an illusion? The only evidence we have of this is when Gwyndolin states, "Thou hast tarnished the godmother's image." This phrase could mean any amount of things. From Gwynevere having just been an image, to him making a reference to archetypes, simply due to him killing a god.
More likely it seems that Gwynevere would be in the flesh when we meet her. She has her own covenant that she can bestow, and like I said before, if gwyndolin is killed first she remains.
It is more likely that Anor Londo going dark is not because Gwyndolin ends an illusion than Gwynevere was a presence that kept it light and she is now dead. If Gwyndolin really was keeping it light as a ruse, then why would he end it once the player killed his illusion. Why wouldn't he immediately through up another illusion and keep Anor Londo light in case any other undead should come looking around.
So for these reasons I don't see Gwyndolin as the grand mastermind, but more of a honorable romantic, like Ornestein. Who, although his mission has become obsolete, continues to carry it out, and attempts to punish the guilty with an undying vigilance. And otherwise, sits by his father's tomb.
Primordial Serpents
For this reason I would have to say Fraampt is the real force behind the legend of the chosen undead and the lord vessel. Lending even more to this argument, he doesn't even bat an eye if you kill Gwyndolin, or any gods for that matter, he just wants to fire linked.
Why?
How should I know, we really don't have any evidence as to what the player linking the fire causes.