Bacteria speeds evolution?

The scientists say the speed of evolution has increased because bacteria and viruses constantly exchange transposable chunks of DNA between species, thus making it possible for life forms to evolve faster than they would if they relied only on sexual selection or random genetic mutations.

Could this mean that, in the aftermath of a global cataclysm, when disease is likely to be rampant due to death & decay, evolution might be accelerated?

And would this fit in with the ascent of humankind since the last cataclysm, circa 10,000 BC?