Accessing DLC without giving Lordvessel to Frampt or killing Sif
From the wikidot:
"Kaathe can be found near The Abyss bonfire after you have defeated The Four Kings, provided that you haven't yet placed the Lordvessel on the Firelink Altar (regardless of whether you have the vessel or not)."
So, it is the act of placing the Lordvessel on the altar that causes Kaathe to not appear, not the act of talking to Frampt.
In order to access the DLC, you need to collect an item from the Duke's Archives, an area only accessible after placing the Lordvessel. So no, it is not possible to access the DLC before killing Sif, if you want to interact with Kaathe in the same playthrough.
There may be one possible way to accomplish this, however: if you get another player to enter your world and give you the Broken Pendant (the item required to enter the DLC). BUT, I've never tried this myself, and after searching about on Google I couldn't find whether or not it was possible.
By default it is impossible to both:
- Join the Darkwraiths
- Unlock the AotA Sif special intro
in a single playthrough.
As pointed out by JMcMinn, you have two conflicting storyline arcs.
In order to join the darkwraiths you must kill the four kings before placing the lordvessel
In order to unlock Sif's special intro, you must free him from the Chasm of the Abyss, which means you need access to the DLC. To access the DLC you need to:
- Kill the hydra in Darkroot Basin, free dusk and talk to her.
- Place the lordvessel after obtaining it to open Dukes Archives
- Kill the golem to obtain the broken pendant
These two actions are mutually exclusive. If you place the lordvessel in order to access the DLC, Darkstalker Kaathe will disappear, preventing you from joining the Darkwraiths. In order to join the Darkwraiths, you must first gain access to the Abyss by killing sif.
Certain items in the game cannot be dropped. The Broken Pendant is one of these making it absolutely impossible to do without modifying your save game to have the pendent.