if the CTD is caused by a script error then the logs will help. but there are a million different causes for CTDs and a lot of them wont have any trace in the script logs
As Amethyst Deceiver points out, CTDs don't get any sort of log, and even if your script is causing the error, you'll find no useful information about the cause of the CTD there. I found this out when I was trying to delete Trap rocks from a script. The game randomly CTDs while disabling or deleting dynamically created traps, and that's all there is to it. No logs. No output. No rhyme or reason.
No awesome breakdown+damage effect for Earth Prison
Mine is for a geographically fixed repeatable ctd. hopefully the log will show a script spawning an item from a leveled list or something like that. there ostensibly a wolf spawn, two bug spans, and a world item spawn in the area in addition to my bandit spans.