No. Your Carousel hidden photos will remain safely stored in your Dropbox account. But, they don't appear in the Carousel web interface or in your Timeline. If you are not using Carouse Web, then your hidden photos will also be hidden from the "Photos" tab on the Dropbox website.
If you hide a photo in Dropbox Carousel and want it again, then you can restore it easily. To restore your hidden photo, open "Carousel app and tap "Menu" located at the top left corner on the screen and then tap "Hidden photos & videos" tab. You will see all your hidden photos. Tap the checkmark located next to any photos which you would like to restore again and tap "Restore" button.
If you want to delete a photo from your Dropbox entirely, then open "Carousel app and tap "Menu" located at the top left corner on the screen. Tap "Hidden Photos & Videos" tab and tap "Select All" button and then tap "Delete" button. You can also delete photos by selecting an individual photos in "Hidden Photos & Videos". By default, Dropbox saves deleted photos for 30 days.