I cannot find a concrete answer as to why Ba'alzamon or Lanfer would want any of the trio to drink in the dream; although many believe that it is most likely not poison, and it could possibly be a ploy to either keep them in Tel'aran'rhiod, or to spike them with Forkroot, or even possibly a way to track them (and giving Mat his brilliant luck).
On the not poison front we have:
On that topic, what was in the goblet? Surely not poison. We know how much Ishamael wants Rand, needs Rand, to fulfill certain prophecies and schemes of the Shadow. Ishamael needs the Dragon in order to complete his plans
Dragonmount - emphasis mine
It does make sense that it wouldn't be poison, Ishameal is smart enough to know Rand (or however they think is the Dragon at this point) needs to stay alive, and can't be killed (at this stage).
On the keep them in Tel'aran'rhiod front: Emily, from Everybody Hates Rand, draws a comparison to Hades and Persephone; in which you cannot eat or drink anything from the Underworld, otherwise you are kept there forever:
Hades and the Underworld once Persephone eats the pomegranate seeds she can’t leave. That also is tied in with fairy tales, literally tales, myths about fairies, where if you go into the world of the fair folk and you eat or drink any of their stuff than basically they can keep you which is freaky...
Everybody Hates Rand Transcript - p14 - emphasis mine
Which would make sense, if you eat, or drink in this case, an offering your soul is therefore tied to whoever gave you that offering.
From the tor reread, and again from Everyone Hates Rand we also note that there is no one reason why any of the trio refuse the drink from either Ba'alzamon or Lanfear (who tries to get Perrin to drink, and he inadvertently refuses the drink when actually refusing the call of the wolves)
And then there’s the blood-red wine that both he and Lanfear kept trying to get Perrin to drink - Ba'alzamon tried to get Rand to drink spiced wine from a goblet in the very first dream he appeared in, and we still don’t know what would happen if anyone actually accepted one and drank from it. Nothing good, obviously, but I really would like more info on what Ba'alzamon—and now Lanfear too—is trying to accomplish. Is the drink poison? Does it establish some connection between the giver and the drinker? Is it like accepting the Dark One but for Forsaken folks instead?
Tor Reread - emphasis mine
The next thing the dude tries to do is get Rand to drink from this goblet of wine, and again, don’t really know what would have happened if Rand had drunk from this. We don’t know what is happening here
Everybody Hates Rand Transcript - p14 - emphasis mine
Regarding the tracking of the trio, we can look to Theoryland, and see that the writer there speculates that although Rand and Perrin forsook the drink, Mat actually gave in:
Pg. 66, 67 Ba'alzamon offers Perrin a drink like he did for Rand in the first book in the Dream (tEotW; pg 203). Perrin declines the drink, and Ba'alzamon’s reaction is the same as it was for Rand. Rage, disappointment, etc. Perrin does this to Lanfear too, right after he does it to Ishamael.
This is Mat's mistake in The Eye. All three of them had a dream in Baerlon, and I think Ba'alzamon killed a rat for all three of them too. They spoke of the dream together, and it was the same for all three. Whether or not all three were offered a drink, we can only guess, but I believe they all were offered drinks (why not?), and that Perrin, like Rand in the first book, turned down the drink as he does twice more in this book. Mat, on the other hand, we don’t know. Maybe he did drink that very first time, and that is what helped Ishamael keep so many of his underlings hounding them constantly
Theoryland - emphasis mine
The writer does go on to say that perhaps it is the knife that is the beacon, but after two days could it really have been that strong of a beacon?
Theoryland continues on to suggest that Mat's luck actually comes from him drinking form the goblet, and therefore forging a link between the two:
Under the influence of the dagger, Mat let down his guard for the fatherly man in his dreams giving sage advice, and a link to the Dark One was forged with a “drink.” Mat now has a very logical reason for his supernaturally augmented luck.
Theoryland - emphasis mine
The writer does go on to say that it's perhaps Mat's luck that allows the Dark One's luck to change and give him this sort of ultra-luck though.
And finally, on the Forkroot front, we can look to an interview with Robert Jordan on Theoryland about whether or not drinking something in Tel'aran'rhiod will affect you in the real world. And if the trio did, then it would perhaps effect them the same way that it would in the real world:
Bradley Staples
Can you explain a bit about the properties of the World of Dreams? Such as when Nynaeve forced Moghedien to drink forkroot tea, which caused the Forsaken to fall asleep. But within that same book, the Wise Ones tell Egwene that drinking tea will in Tel'aran'rhiod will cause no effects upon the body.
Robert Jordan
It's a strong matter of belief. If you believe something like that will happen to you, then it can and does.
Theoryland - emphasis mine
So we can conclude that we really don't know why Ba'alzamon or Lanfear want Rand (or the trio) to drink anything, but there are some speculations.
Personally, my belief is that it works similar to Persephone and Hades, and that consuming something offered by these two will somehow 'link' them together, and allow them to be tracked or influenced against their will.
