I don't think this is correct. My impression has been Peter the Roman will be a strong Pope who will lead the church in desperate times. The man of perdition, the antichrist, will attempt to take the throne of Peter illegitimately. If that will happen during pontificates or in between, I don't know.
I would also point out that there is a break in the lineage of St. Malachy. Peter the Roman is clearly an addendum. There is no reason to be certain that Peter the Roman will imediately follow The Glory of the Olives.