I'm not sure what you mean by "general application logging" vs "debugging".
I personally thing TMS Logging has too many specific fields. A logging framework imho should log raw data, the processing of data is done out of scope by other tools.
You can log objects, either directly using LogObject or serializing an object yourself. You can then filter data by properties in those objects, or by searching a specific subtext, or any other similar mechanism.
No, that's not possible.