title says it all - I presume roughly that if you have ASICs then Botnets cannot muster enough power to compete. Is this correct?
No, ASICs have nothing to do with botnet formation.
However, botnets are less likely to target a coin whose PoW has ASICs since
ASICs will only be developed when they significantly outperform CPUs&GPUs,
which limits profitability compared to ASIC-less PoWs/coins.
But as we saw recently (
http://www.zdnet.com/nas-device-botnet-mined-600000-in-dogecoin-over-two-months-7000030662/), botnet operators can be either dumb or lazy
and still go after BTC/LTC/DOGE.