How completely is completely, really? He'd keep the king as a prisoner, obviously, but the Persians would crown another one and remain a problem. How much of a problem will depend on Roman policy and luck, given the potential for territorial concessions, playing off factions, and turning client kings. I can't see the Sassanid empire just falling apart, but it could certainly be much diminished.
Beyond that, there is still a lot of repair work to be done. The mid-third century was a volatile time and Roman superiority not to be taken for granted. Valerian was not a soldiers' emperor. Any reverse could count against him. If he survives the critical years after Edessa, though, he has a good chance of securing an untroubled succession for Gallienus, who would probably be remembered very differently.
Whether he, in turn, can secure the imperial centre and break the cycle of acclamation and civil war remains open. I don't think so, but then, Diocletian did, so it's not impossible. Given the state of our sources, it is hard to get an good idea of his real character. Seems to have bneen tough and not scared easily, which helps.