I do not see almost any mechanism by which that should be more likely. As stated in the first post, there are no gameplay changes which do not come via the de jure changes in this mod, and the HRE is de jure approximately the same as Vanilla in start dates other than 867. In 867, if the AI creates the HRE (which requires to hold the Empire of Germania as well as the Kingdom of Italy, hence it is much less likely than in Vanilla) the kingdom of Italy - including Latium and Rome - de jure drifts immediately to the HRE. This possibly makes it more likely; I do not know how the AI is coded in that respect so I cannot really tell. Do you observe this pattern under those circumstances?
If this were the case, let me say that I would not be that unhappy about it, as my modified "Create HRE" decision is aimed at simulating the political status of the HRE in the 10th century, when the Emperors were on the verge of having their authority supersede the Pope's (some of them even resided in Rome). Ideally however, I should also have some mechanism by which de jure control over parts of Italy is lost for both the HRE and the ERE, so that the Empire of Italia can (potentially) appear even in the 867 start date.