I think a little degree of nuance is needed here.
"... destroy Christianity and you destroy civilisation" might seem to imply that if a civilisation isn't Christian, it isn't civilisation. That is clearly false. 

On the other hand, perhaps you mean that a civilisation that is built on Christianity might have difficulty surviving without Christianity. I would be inclined to agree with that.

However, that leads to a subsequent consideration: what kind of Christianity is needed within  a "civilisation" that has been traditionally "Christian"? Is it always as it has been in the past? 

For me, one of the reasons why the Church held Vatican II was to begin to look for the way to be Christian in and for the modern world.