There is nothing in GFII to indicate the family's decline.
The remark about the Roman Empire referred to the loyalty, integrity, and continuity of that Empire at its height and how Michael's style of governance imperiled that integrity and continuity inthe Corleone family.
Agreed, as far as the bottom line of business operations is concerned (hence my qualification, "of some kind"). Indeed Tom's remark in question comes after he 'reminds' Michael that "he's won."
At any rate, I think your suggestion about what Tom was referring to is plausible.
