This depends entirely on what is meant by "collapse". If a setback to medieval times is not considered a collapse then we will be fine.
CommunistDog (left his/her comment under "No" vote): Our consumer society consumes resources at an ever accelerating rate. In fact, for our modern society to even persist, this resource consumption is absolutely necessary. These resources however are finite and will eventually run out. How are environmental groups going to change this?
One world gov't, as soon as we're done with all these petty conflicts in between humans, we can move onto space exploration. And after colonizing the galaxy, we'll ensure that our species will survive for a long time.