Not exactly, at least with barbarians. Played last night as the Greeks, had two warrior units off to battle those filthy barbarians (which all yielded horseman units, allowing me to put together a horseman army rather quickly). Meanwhile I'd produced a galley and dispatched it to get at those artifacts early and had my unoccupied city producing a hoplite unit. I'd also been the first to research Masonry and had the complimentary wall built around my city.
None of it mattered when an American warrior unit parked itself outside my city. Lincoln suddenly declared war without asking for anything in return, which I thought was strange, until I was advised Athens had fallen. D'oh! Seems the AI knew that I had no one in my city, which is a bit of a cheat when you think about it (without using any Ranger skill...)
But as for the barbs, only had them bum rush a city once, but had enough time to rush a unit to defeat them.