I don't think the BBR feature is directly effective against Sybil attackers. It prevents disclosure to the public (for example by someone spending without a mix) but a Sybil attacker can easily create these min-mix outputs, and then you will choose them as your "safe" mixin. But the damage is done as soon as you use the attackers outputs in a mix (he knows his are not the real ones so yours is identified by elimination); whether or how he spends does not matter.

The BBR feature may slow down the rate of chain reaction sunder some conditions, I'm not sure.