Ok, this theory is really, really silly. It doesn't answer any questions, and only leaves every question in the game unanswered. That alone should be proof enough that it is not a good theory, but, I took the time to disprove it.
Like other people here, I thought there was no way to actually disprove it, though. However, when looking at the very premise of it, I noticed that the weak point is the actual death of Squall.
Here are two screenshots of the opening of the game, the Squall/Seifer fight. This happens in disc one, and it's not a flashback, dream, or anything. It happens before you are able to control squall, and immediatly afterwards you wake up in the nursery, with a cool looking scar on your face. Point is, this fight happened, and it's not a dream or hallucination according to the Squall's dead theory.
Look at that. Blood. Lots of it. Blood on the floor, and on Squall's face. Unlike Aeris' death, where Sephiroth's blade is clean, and Aeris herself is clean when Sephs takes out the sword from her, FF8 isn't afraid to show blood. The original FMV is here
FF8 Squall Vs. Seifer - YouTube
But Youtube links to game videos are fickle, so I decided to put screenshots instead.
The point is, when you get cut in FF8, you bleed, and you get a wound.
Now, the main idea behind this theory is that, from the start of disc 2, Squall is dying. Here's a quote from when you wake up in the prison after the Edea attacked you with the ice shards.
So, let's see the FMV where Squall gets impaled by those ice spears.‘(...Where am I? I...challenged Edea... My wound...? No wound...? How...? The Galbadian soldiers... ...We were surrounded. He was there... Seifer, leering down at me.) "Damn you, Seifer!"’
No blood on the spear.
No blood on the floor.
No blood on Squall's clothes.
Again, here's the FMV
Final Fantasy VIII - Edea Strikes Squall with Ice Magic - YouTube
So, the answer to Squall's starting question in disc 2 is:
There are no wounds because there was no blood. There was no blood because those were magic icicles that don't really kill people, just make them unconscious, like all those ice spells you drew from monsters all time.
In one FMV you get a little cut in your forehead, Squall, and you bleed like a mothersmurfer. When you got impaled through your chest? And probably compromised your lungs, heart, or maybe stomach? Nothing. The conclusion is that you weren't really impaled with something palpable. (do note that only one icicle is seen impaling Squall, even when Edea shoot several. The others maybe missed, or maybe went through Squall other organs).
So, no, Squall is not dead from disc 2 forward.
QED