Thanks for the tag @Samuel Pavlovcik
Chicago permitting is more of an art than science. The biggest factor is the motive in applying for repair/replace as opposed to plans/permits.
I'll preface my thoughts by saying that you should always pull the correct permits for your job. The risk is not worth the reward. A lot of people pull repair/replace to save time and money knowing full well that they will be performing work outside of the permit requirements. Quite simply, it's a tactic to post a permit card in your window so if a neighbor calls or an inspector drives by they will see that the city has permitted work at the residence. If they decide to dig deeper and perform a site visit, it will become a costly mistake (time & money).
Previously, inspections for a repair/replace permits were unheard of. Now there are specific things that will trigger an inspection (i.e. electric/plumbing/HVAC). If you're trying to accomplish the scenario above, keep the application limited to windows/doors/cabinetry/trim/etc...the city doesn't have inspectors for those items.
What you don't want to do, is a bunch of work outside the permit and invite inspectors to the property to see what you've done. You either pull the correct permits or lie. There's no middle ground.
My last plumbing inspection was about a week or so ago. The inspector called my plumber, asked him if he did the work and then passed us without performing a site visit. We had pictures throughout the process as a precaution but we didn't end up needing them.