Is it possible to list running processes that are not signed or notarized?
You will need to write a short script to gather this information.
Obtaining a list of processes is possible with ps and code signatures of processes can be checked with codesign.
codesign
The codesign command can be passed process identifiers, pid. To verify the signatures of two running processes call:
/usr/bin/codesign -d -vvvv 279 422

The flags are:

-d for validation
-vvvv to increased verbosity
279 the first process identifier to check
422 the second process identifier to check