Any time any program executes instructions, those CPU cycles are unavailable to any other program, just like any system resource.
However, there is little or no practical relationship between the journal entry processing done by your programs and the database processing going on in other jobs, as long as your journal programs don’t also access the files directly.
If you have a program that receives journal entries for a particular file and there are no processes that are updating that file, then your journal program won’t be taking up any significant system resources at all. It won’t have any work to do — it’ll just be waiting. There will be no impact on any other job.
If you have a process that’s generating 10 journal entries per second against that file and your journal program receives individual entries, then your journal program will be called 10 times per second — assuming it can complete its work that fast; it might lag behind if it’s inefficient. If your journal program has requested a block of 10 entries, then it will only be called once per second, on average. (Not exactly, but that expresses the idea.)