Well, coming back to the initial question of the OP, if an other emperor could rule longer.
Let's assume that Antonius Primus had no agreement with Vespasian and his delay was unintentional. So he attacked Vitellius in the name of the already beaten emperor Otho. Afterwards he conquered Rome, and now he heard of Mucianus marching to Italy. So he decided to surrender, gave the command to Mucianus, when he arrived. And of course he claimed, that he always fought for Vespasian. Sounds a bit weird to me.
Actually, Mucianus blamed him for his attack on Vitellius and Rome, and sent him to Vespasian, who was in Egypt this time. Vespasian honored Antonius Primus and sent him to retirement.
Now, what happens, if Antonius is loyal to Otho and is not delayed? Otho should win the Battle of Brediacum. Vitellius is defeated and the Rhine legions support Otho from now on.
Now Mucianus arrives in northern Italy. It is obvious, that Mucianus, who marched via the Hellespontus, started marching long before Otho was dead. Had he really orders from Vespasian to reenforce Otho? And why was Vespasian in Egypt at this point of time to control the grain export? Honestly I do not believe, that Vespasian was not planning to fight Otho.
But in our new scenario, with the Rhine army, the pannonian army and the praetorians, Otho has good chances to defeat Mucianus. Just if Mucianus really fights. Vespasian can simply block the grain support from Egypt and Otho is in serious trouble.
So finally it all comes down to 2 questions:
1. Did Antonius Primus have an agreement with Vespasian, when he marched to Italy?
2. Was Mucianus by order of Vespasian (initially) on his way to Italy to attack Otho?
I am convinced that yes in both cases. But I have to read a bit more about this civil war, before I could come to a final conclusion.