Does OBS produce auditable log files?

Yes, OBS has very good logging capabilities for reviewing the startup environment, hardware status, and recordings.

Default Log Location

C:\\Users\\%USERNAME%\\AppData\\Roaming\\obs-studio\\logs

Sample Log Data

Startup & Machine Specs

22:19:47.822: CPU Name: Intel(R) Core(TM) i7-5960X CPU @ 3.00GHz
22:19:47.822: CPU Speed: 2993MHz
22:19:47.822: Physical Cores: 8, Logical Cores: 16
22:19:47.822: Physical Memory: 65454MB Total, 37817MB Free
22:19:47.822: Windows Version: 10.0 Build 18362 (revision: 657; 64-bit)
22:19:47.822: Running as administrator: false
22:19:47.822: Aero is Enabled (Aero is always on for windows 8 and above)
22:19:47.822: Windows 10 Gaming Features:
22:19:47.822: Game DVR: On
22:19:47.824: Sec. Software Status:
22:19:47.828: Windows Defender Antivirus: enabled (AV)
22:19:47.830: Windows Firewall: enabled (FW)
22:19:47.833: Portable mode: false
22:19:47.951: OBS 21.1.0 (64bit, windows)
22:19:47.951: ---------------------------------
22:19:47.953: ---------------------------------
22:19:47.953: audio settings reset:
22:19:47.953: samples per sec: 44100
22:19:47.953: speakers: 2
22:19:47.955: ---------------------------------
22:19:47.955: Initializing D3D11...
22:19:47.955: Available Video Adapters: 
22:19:47.957: Adapter 1: NVIDIA GeForce GTX 1080
22:19:47.957: Dedicated VRAM: 4081057792
22:19:47.957: Shared VRAM: 4252487680
22:19:47.957: output 1: pos={0, 0}, size={3840, 1600}, attached=true
22:19:47.960: Loading up D3D11 on adapter NVIDIA GeForce GTX 1080 (0)
22:19:48.047: D3D11 loaded successfully, feature level used: 45056
22:19:48.876: ---------------------------------
22:19:48.876: video settings reset:
22:19:48.876: base resolution: 2560x1440
22:19:48.876: output resolution: 2560x1440
22:19:48.876: downscale filter: Bicubic
22:19:48.876: fps: 30/1
22:19:48.876: format: NV12
22:19:48.876: YUV mode: 601/Partial
22:19:48.883: Audio monitoring device:
22:19:48.883: name: Default
22:19:48.883: id: default
22:19:48.883: ---------------------------------

Recording

22:21:40.648: ==== Recording Start ===============================================
22:21:40.648: [ffmpeg muxer: 'simple_file_output'] Writing file 'C:/Users/User1/Videos/2020-03-11 22-21-39.mp4'...
22:21:43.935: [ffmpeg muxer: 'simple_file_output'] Output of file 'C:/Users/User1/Videos/2020-03-11 22-21-39.mp4' stopped
22:21:43.935: Output 'simple_file_output': stopping
22:21:43.935: Output 'simple_file_output': Total frames output: 84
22:21:43.935: Output 'simple_file_output': Total drawn frames: 99
22:21:43.936: ==== Recording Stop ================================================

Please download a sample OBS Log file for a complete review.