IMO that’s too technical. I think the empire started when they took over all of Italy, Gaul and North Africa, maybe after the Punic Wars.
Wasn’t Julius claiming the title of Imperator and didn’t they already expand into Egypt. I would associate the word with the fact that Roma controlled an empire.
“Imperator” was a military honorific - see http://en.wikipedia.org/wiki/Imperator
I can’t argue with your reasoning, but it may be that prior to Augustus the Roman Senate still had some actual power.