That depends entirely on how you set up the content.
If each product is on its own page, you can delete the whole page, and the other pages will reflow (but you will have to be careful with your layout to avoid left-right page issues)
If everything is in a continuous set of linked text boxes, and all images are inline, it will auto-adjust.
If you set it up as a continuous table, with each row containing one product, it will also auto-adjust.
Other than that, I think you will have to do the work manually.
It depends on how you set it up. One way is to anchor your catalog elements in threaded text frames so as you add or delete items all that follow flow forward or back, just like paragraphs in a word processor.
Does InDesign have an option to have catalog pages auto adjust...?
While InDesign has the capability to handle content as I described above, it wouldn't be accurate to think of it as "an option." It's not something you can turn on and off as desired. As the layout artist you must employ the strategy at the outset of the project and propagate it throughout via your methods. InDesign has features which facilitate it.