Sure it can; there's nothing intrinsic to the ALliance that makes it incapable of carrying a plot; it's just a matter of execution.
A story is a machine; it has components that interact, you input characters, mix in some conflict, and mash it around until you get some form of entertainment. Like a machine, any of these elements can enhance or detract from the output.
With the alliance, the problem is mainly a lack of internal conflict, coupled with a deficiency in characterisation. Fortunately the solution is simple, all Blizz need to do to make the Alliance interesting and capable of carrying great plotlines is to invest more time defining and expressing key characters in the Alliance, and to make them want different things to one another.
Have Greymane flirt with the Scarlet Crusade remnants and characterise him with increasingly alienating zealousness in expunging the Forsaken not only from Silverpine, but where-ever they're found. Standing by him would be the newly militaristic Jaina, whose faith in peace and the Horde has been replaced by a very tender wound. Across the aisle stands Velen and Mekkatorque each suing for peace and understanding against the majority, albeit for different reasons. Velen very much believes in mercy, forgiviness, and unity as children of the light. Mekkatorque on the other hand is tiring of sending his people to die in a seemingly endless conflict with no advantage to gnomekind, and no reclamation of Gnomeregan in sight. He is seriously considering dropping out of the Alliance all together; only his ties to the Bronzebeards stay him from doing so, but theur influence on Ironforge is slipping.
Moira is rallying more and more of the disparate Dark Iron factions under her son's (her) rule, bolstering what was once a dismissable refugee faction into a comparable force within Ironforge alongside the Wildhammers and Bronzebeards. Anti-dark-iron sentiments are rife, and the inevitable issue of Dagran Thaurissan II's succession is a divisive one. Moira herself is overtly pursuing a 'Dowager Empress' role, with credible threats of civil war being the only thing that prevents this fantasy from coming to fruition, for now. Peace remains in Ironforge, for now, but the tension is thich enough to cut with a knife. Tyrande wrestles with internal questions of confidence in her rule, with accusations that she is a supplicant to Varian's will, and is not the ruthless leader she once was. Though in her heart she trusts in Varian, and supports Velens lofty hope for peace in Azeroth, she is deeply conflicted; part of her truly wishes to do the popular thing and mobilise Darnassus at full capacity to purge Kalimdor of the Horde, abandoning the defensive front entirely.