No. The web server logs are generally more useful than the ones for Portal, but either way it's difficult to tie requests together with logins.
ArcGIS Server logs here have always had so many meaningless "SEVERE" errors they are useless. (And several support calls rendered no assistance on this. The server works, so we continue to ignore them.)
Logging has always seemed like a weak point in Esri. I think they just want you to buy the "Monitor". We can't afford it.
