Well, they were able to subdue Italy.
Easily at first. Then easily at the very end.
After all, that's the very reason Otto I became emperor. The Ottonians pretty much ran northern Italy. In fact, the HRE was made up of the Kingdom of Germany, Italy, and Burgundy united.
And Henry III made and unmade popes as if they were German bishops, interfering south of the Alps at will.
It was only Henry IV onward that the Germans had trouble retaining control south of the Alps.
And even after him, Henry VI and Frederick II managed to control Naples and Sicily, though of course they weren't part of the HRE. It was only after 1250 that the Hohenstaufen control of Southern Italy desintegrated.
And even after that, Emperor Charles V pretty much controlled most of Italy. And if Charles V bequeated Italy to Ferdinand rather than Philip, there's no reason why the Emperor won't be able to retain control over Italy. Later on, Emperor Charles VI got control over Sicily and Naples, though he later lost it. But he got Milan, and later on, Francis I brought Tuscany into Imperial control.