I'd say no, because the chances of a; the war lasting that long, and ;b, the Lombards shattering the central European power equation and invading at the best possible time, were pretty small from the vantage of the early 530's. Furthermore, an Italy that was allowed to recover and adjust would end up not only paying for itself, but also contributing to the revenues and manpower of the ERE, as the African example showed. This means that, to the extent that Italy would have dispersed resources away from the rivalry with Persia, it would also have contributed resources to that struggle. Finally, the political benefits of conquest, while uncertain, should not be discounted. They could potentially include both purely political and knock-on practical consequences, such as, an ability to better dominate the Balkans because the Romans would have armies on its southern and western boundaries, greater influence over the Western Church enabling a more coherent religious policy, lessons in the Italian war and the reintegration of the peninsula being used to improve the army and bureaucracy, and so on. In conclusion, I'd say that, from the perspective of Justinian, (or, indeed, any well-informed observer) at the time of the invasion, the ideological benefits would have most likely been ultimately accompanied by material and second-order political positive effects, and the cascade of disasters that was the OTL result was rather unlikely.
