Yes, you can delete log files on your device...
Using the app SD Maid (Explorer tab) on a rooted Samsung Galaxy Note 1 (N7000), Android 4.1.2, LT5 Build, I found 900+ log files in /data/log.
After clearing the literally hundreds of dumpstate* files, I got my internal memory back from only 207mb up to 1040+ mb! Now I can complete all the missing updates. These files were dated back over more than 1 year and seemed to serve no valid function any more. Afterwards the device booted, was faster and no functionality was lost.
Looking at the dates of these files they coincided with some system crashes and SD card mounting problems I had received in the past.
But in order to even see these files you will need a rooted device.
Using the clean master app on a rooted device also found a lot of files which could be deleted.
Here are the links to the Apps in Google Play Store as requested