Session Tracking in the ASM

Yes, ASM maintains state information with the Main ASM Cookie, the TS Cookie, and this is tied to the sessionID you see in the event logs.

I do not believe the sessionID itself is exposed via an irule however (see the page on ASM::violation_data), however, you should simply get this information logged remotely anyway when you use remote logging, without needing to extract it within an iRule.

Have a look at this manual on Logging Application Security Events.