abuse.ch: How Big is Big? Some Botnet StatisticsWhen Ive started to sinkhole this botnet I was shocked as I saw that more than 1,2 million (yes, 1200000) unique IPs connected to my sinkhole just within 24 hours.
about.com: BotnetsAccording to a study by McAfee, "at least 12 million computers around the world (are) compromised by botnets."
Even if all coins were mined by botnets, it does not directly lead to collapse. You have to read the paper though to understand why the authors claim this.
Several things happen: (a) incentives for easy money naturally cause an increase in criminal participation at all levels, such as direct theft of bitcoins. This increase across the board encourages (b) honest users to pack up and leave. Both of these effects combine to create rising criminality, and (c) at some stage the Feds get involved. Finally, (d) the system collapses.