Saw also the old mini-serie. But now, when i think about it, i cant understand, why the Old Woman send the quartet do Las Vegas? They did actually nothing important. This freak playing with fire did.
Well, on a symbolic level their journey to Vegas shows that they had the faith in God and perhaps that humanity was worth saving. That's the titular Stand the characters are making; Mother Abagail atones for her excessive pride by speaking directly for the Lord, and the chosen four represent humanity's best characteristics as proof that this crazy species called Man is worthy of continuing on, even after a near-apocalypse. If the four didn't make their stand then New Vegas probably finds a way to blow up Boulder before eventually blowing up themselves.
On a practical level, the murder of Glen Bateman causes Flagg to start doubting himself even more which makes his powers more unstable. If he had a better grasp on his magic then he possibly could have prevented the lightning he summoned from being used against him. Ralph and Larry's public execution also gives a reason for everyone in New Vegas to gather around in one spot. If the sentries were still out on patrol as opposed to witnessing the supposed execution, then they would have killed Trashcan Man on the outskirts of Vegas and the Hand of God probably would not have been able to detonate the nuke.
Trashcan Man could also have been an envoy of God. The Lord works in mysterious ways, at least so the old saying goes, and many of his actions from torching the fighter jets to bringing the nuke to Vegas directly benefitted Boulder and humanity. His "My life for you" catchphrase could actually be a red herring; instead of being in reference to Flagg, it could actually be something he repeats to God, whether he is aware of it or not.
Edit: One last thought - the three spies that the Free Zone sent over also caused Flagg's confidence to erode. The Judge's execution shows that Flagg doesn't have full control over his minions and followers, Susan Stern's defiance of Flagg and her suicide show him that he isn't able to use his powers completely to his own whims, and Tom Cullen's presence shows Flagg that he isn't able to read everyone's mind and makes him lose trust in his followers since he thinks anyone could be the last spy. These all contribute to his downfall once he starts over-extending his use of magic and loses control of the people of New Vegas.