If you do this, make sure that you're not Suffering from Buffering. Else Process 2 might think that you're on a job previous to the current one.

I'd also suggest that if you've taken the above step, then Process 1 should write additional information (eg timestamps before and after any batch step)) to the log. This has no immediate relevance to your problem, but if the batch process gets slow, those timestamps will let you figure out which steps are performance problems. Build it from the start, and when you need it, it will be there.