I've read about that contributing to the fall of their empire before - I guess we'll never really know, but if it did then the impact of that element on human history must be massive.
I'm no historian, but I don't think more wars would have been the problem - they had plenty of wars before their downfall. If anything I thought things got worse once they were expanding less, because they no longer had an influx of resources from conquered territories.
Wikipedia puts it out as an option: http://en.wikipedia.org/wiki/Fall_of_the_roman_empire#Lead_p...