Central and Western Europe have been farmed for thousands of years by that point. Farming in Southern France/Iberia was already well established around 7000 years BP (before present). By the time of Romans, the hunter-gatherer's lifestyle was wholly displaced from the area, with only minuscule fraction of resident population engaging in it, at best.
After all the grain has been stolen, you are in for a rough year where hunter/gathering might reappear + cannibalism. Imagine it less as a "civilization appears" moment, and more a "metal locusts from outer space eat previous civilization and leaf behind large slave farms after years of famine.
That's what I meant: I take it as a given that if they were successfully invaded, they must have left the hunter/gatherer state behind, likely by a considerable margin.
