You misunderstand. I meant they would know it was coming a lot sooner than three years before it happened. The timeline doesn't add up.
Would they though? We've been studying our own star for thousands of years and it's only in the last few decades that we've really stared to grasp how the thing works and what it's doing.
Now I'm not certain how long it takes for a binary system to reach critical mass, but given that the Dilgar homeworld was able to evolve life at all it seems likely that this is the first time it'd ever happened. They'd have no point of comparison. Those two stars are the only ones they'd ever known and they may not have realized what was happening until relativity recently.
Really though, we have no idea *when* they discovered their planet was doomed. For all we know they could have figured it out only a few decades ago or a few centuries. Maybe it just took them that long to get to the point where they felt confident they could take on the other minor races and survive. Indeed, I'd put money on the truth being a closely guarded state secret and anyone trying to raise the alarm would have been quickly silenced. Indeed, the best evidence for this is that their surviving forces (assuming there were any) went back to their home system after the invasion failed. The only one who didn't return home was the invasion's supreme commander, who would logically be the only person in the know besides their ruler(s).
I suppose the logical question would be why the leaders didn't attempt an evacuation like Earth did before the Battle of the Line? Maybe they did, but then again maybe Earthforce blew up their jumpgate, stranding them in their home system at relativistic speeds and unable to outrun the blast wave. On the other hand maybe their calculations were off and they didn't think the star would blow for another century.
You're assuming the serum worked as advertised. We don't really know that, all we know is it extended Deathwalker's life somewhat. And as we saw, its purported properties could make it an exceptional agent of chaos. I could see it as a Shadow tool.
In the short term, sure. But as I said, in the long run it'd lead to a stagnant state of affairs and therefore not something either the Shadows or the Vorlons would want. Remember that the Shadows don't believe in chaos for the sake of chaos. They believe in chaos as THE driving force of evolution. The scenario Jha'dur described was quite the opposite: an evolutionary dead end.
As for whether of not it worked the way she said; the initial tests came back positive and clearly the Vorlons were convinced enough to openly off her. Really, we have no reason to believe otherwise.