Well, could it at least buy some time for the Holy Roman Emperor to focus on building his powerbase in Germany, or making conquests in Baltic pagan lands? Perhaps that could allow future HREs to extend their influence back into Lombardy when German kings have more resources at hand.
Rainald's presence certainly didn't make anything easier for Frederick or buy him any more time. As mentioned, it's the policies of the empire that created the resistance, not the identity of the man who was promulgating them.
A lot of this depends on the manner of the Lombard League's "defeat." A defeat in the field, like a reverse-Legnano, is a setback for the League but doesn't destroy it. After all, in a previous campaign Frederick had actually conquered and destroyed Milan, and yet the city had been rebuilt and resistance in Lombardy only grew stronger. The problem for Frederick is that he simply doesn't have the men or the native support in Lombardy to keep the whole region under his thumb. A year's campaign is scarcely enough to besiege and reduce a single city, and he has to go back to Germany regularly. Passing the responsibility to some sort of lieutenant doesn't change the fact that imperial power in Lombardy rests upon the exertions of German knights, who have little reason to be in Italy if the emperor isn't leading them there. Initially, when Frederick was merely campaigning to humble Milan, he had the support of anti-Milanese cities and their armies (e.g. Pavia, Cremona, Lodi), but once the mask slipped and it became plain his ambitions were grander than just beating up Milan even these communes abandoned him, forcing him to rely almost entirely on German forces (with some modest support from the "native" territorial nobility, particularly in the northwest).
What if the hypothetical Viceroyalty in Italy becomes a dumping ground of sorts for uppity German lords, who end up being too busy fighting the particularist cities of Northern Italy (their own vassals) to actually challenge the emperor?
Where are they "dumped," exactly? If the emperor himself can't subject the cities to his will, what makes you think some exiled German nobles could do it?
I mean, in a sense this happened - Frederick gave Tuscany and Spoleto to Welf VI, a Bavarian, who had previously rebelled against the crown. It didn't help very much.