The right thing to do would be to talk to the accuser, since she's said she's willing to cooperate. If her claims seem credible, then they should meet with Brown and get his side of the story, and review his claims of extortion. If her claims appear credible, and his do not, then they would have cause to put AB on the exempt list while conducting a further investigation. The NFLPA would have to go along at that point.
Otherwise, if his specific extortion claims seem credible, they could simply conduct the investigation while Brown plays, or defer it to the offseason unless new information comes to light.
There are obviously two flaws with this line of reasoning: (a) it's unclear how much the NFL can investigate while there is ongoing civil trial, which will take years to resolve; and (b) it ignores the outside forces that drive the NFL and Roger's decision making when it comes to player discipline. And, we really don't know what the accuser means when she says she's willing to cooperate; she could very well lawyer up between now and Monday. So could Brown.