Can you verify that from Procopius?
(Sorry for the bad translation, I can't find the text in English)
There's an hint of Belisarius divergences in chapter 22/4.
As soon Justinian knew the king of Persians broke the truce, he decided to make peace ith Goths, and to call back Belisarius to give him the command of the Eastern army. He gave their leave to Vitiges' envoys, that where in Constantinople, and promised them to send of his own in Ravenna, to negotiate the peace in fair terms for both nations.[...]
But most of it is in the chapter 29.
Dominicus and Maximinus, senators of Constantinople and evoys of Justinan, then arrived, with capacity to make peace, if Vitiges kept half of his treasury and would rule in the country, beyond the Po, and that the Emperor would take the other half of treasury and would take tribute of all the land on this side of Po. These envoys, after having communicated their letters to Belisarius, went to Ravenna, where Vitiges and Goths accepted the conditions.
Belisarius grew immensly unpleased, that the honor of a plain and complete victory was taken from him, and that he was deprived from the glory of a new triumph. When the envoys came back from Ranevva, he refused to confirm the peace treaty, and filled, by this refusel, Goths of suspicion and defiance; as such they argued they wouldn't make peace if Belisarius wouldn't sign it and would swore to maintain it. This general, told that there were leaders that accused him to be unwilling to end the war because of schemes he was involved in against the Emperor, gathered all the commanders, and in presence of Dominicus and Maximinus, spoke them so.
I know enough, and I think you know as much as I do how much war success and uncertain and dubious. The hope for victory is extremely decieving. It flee to who think hold it, and switch side with who were seemingly defeated. It's why when peace is discussed, not only reasons that gave oneself the advantage should be considered, but also infidelity of luck and instability of events. It's what forced me to gather you as for we'll examine cautiously what's more advantageous for the Emperor's interests, nothing could be blamed on me anymore, as there's nothing more ridicule than being silent when there's a lot of possibilities and there's liberty to choose any as we would want; and then to shout and blame, when happens some unfortune. You know what are imperial tought, and what is Vitiges' resolution when it come to peace. If you are really certain it is useful to the State, please tell it so without fear. But if you think it is possible to take all of Italy and to destroy all the Gothic power there, don't hide your opinion.
After this speech, commanders declared they shared Justinian's opinion, and that for them, nothing could be done anymore against the ennemy. Belisarius asked them to write down their opinion, as they wouldn't be able to deny him, which they quickly did.
While this happened among Romans, Goths pressured by hunger, and bothered by the rule of a ruler as unfortunate as Vitiges, didn't surrendered only in fear of being enslaved and deported to Constantinople. The more powerful among them discussed to give the kingdom to Belisarius, and begged him to accept it. Nothing was further than the general's will to make himself king without Justinian's agreement, who he pledged obedience, and he had a natural aversion of tyranny. He still pretended to consider barbarians' proposal, in order to benefit from it, altough Vitiges wasn't pleased at all. He was opnely overjoyed by this and reasurred Belisarius that nothing was to fear from him. Then this general gathered once again all the commanders, and asked them if it wasn't a great advantage to take Vitiges, to take all Goths as prisonners, and to rule over all Italy. They cofnessed it would be an immense benefit for the Empire, and asked him to do all of these things if he knew how. Right then, he send trusted people to Vitiges, and to the nation of Goths, to ask them to do what they promised. As hunger didn't allowed them to hold out any more, they sent envoys to Romans, with orders to speak only to Belisarius, to make him swear that they would be unharmed, and that he would be king of Italians and Goths, and then to go to Ravenna with his army. Belisarius promised, taking an oath, everything the envoys asked from him, exception made of what mattered to the kingship of Italy, on which he said to them, that he would swore to Vitiges and Goths, and that he would put his word on any oath they would ask from him. They couldn't concieve that he would be willing to refuse a crown, thinking he passionately wanted it, invited him to come in Ravenna. Then he sent Bessas, John, Narses, that he considered as personal foes, each on separate place, to search for weapons as there were not in the land they came alltogether. They obeyed to his orders, and went with Athanase, recently arrived from Constantinople.
When I witnessed the entry of the Roman Army in Ravenna, this tought came to be that neither virtue or strength, or by having more men that great things are achieved, but by a hidden decision of God that make do as he wishes, without encountering any obstacle to the execution of his will. While Goths outnumbered Romans in number and strength, while there was no fight after city's doors were opened, and that there wasn't anything before them that would terrify them, they nevertheless submitted to the rule that was imposed to them by an handful of people, and this rule wasn't unsupportable for them
The Ostrogoths had been badly beaten and would have lost most of their kingdom. I think that your prognosis of their chances in a renewed invasion after that are optimistic. Besides, the Empire would have left a garrison. Had peace been signed, I don't think that the Goths would have broken it lightly.
At this point, still, Justinian have to deal with a troubled situation in Persia and needs troops and generals. It's possible that Romans would have eventually needed to rely regionally on Gothic's good will that would still have held a rich land relatively untouched by war (Frankish campaigns in Italy so far having been more small scale raids, and not really successful ones) and, which might have been problematic too, in connection to other Barbarians as Lombards or Franks that, would the Roman armies gone away, wouldn't have felt as threatened by imperial retaliation.
Even in less than favourable's conditions, IOTL Totila did a great job taking back the initiative for Goths (it could be argued that without Theodabald, Goths would have put more of a fight right from the beggining), so I don't think that Belisarius was that wrong arguing that Goths could have taken back ground from Northern Italy at all. Now, if campaigns against Persians are quick enough, I agree there's much less chances for Goths being able to pull something on the long run.