You can search for campgrounds while offline in the same way you do while online. But make sure you have the offline map downloaded before leaving a "no data area", or it won't show up or be searchable at all.
In the app, you need to select the Profile icon at the bottom and then navigate to the PRO TOOLS tab. There you will see the options for "offline maps" and "map downloads" Your phone and the app should automatically update the offline database (campground database) any time you sign in or open the app, but please make certain before you leave a cell area. Once you are out of cell range or wifi range, you will not have the option to load this or offline maps since you do not have a signal. It will only work offline if you have loaded it before you go into a no signal zone.