Oh, goodness, no! It would take over a year for them to arrive! If it took armies that long to travel, then by the time Elrond was sent for, if the siege had already begun, the war would be over, and he'd arrive to a dead and black neighborhood! Well, maybe not quite to that extent...
I don't know anything about the times, dates, or when and where people were according to Tolkien or what (because, frankly, I know very little history), but I just wanted to say that it is difficult to move great forces and we have to keep that in mind...well, you, I guess, who ever is going to be writing it, or whoever knows the dates.
-Folwren