Can I use apps other than Photos with Apple’s SD-card reader? I have an iPhone 7 and I’m considering buying the Lightning SD Card reader that Apple makes. Is it possible to access the SD card’s files using apps other than Photos—for example, Dropbox?

(My specific use case is that I’m going to be traveling and I want to back up my photos to my phone. I’d like to back them up somewhere online, too, but I don’t use Apple’s photo-syncing offerings and I’d prefer not to turn them on just for this situation.)
Apple's camera-connection hardware only interfaces with the Photos app, unfortunately. However, you should be able to transfer the photos from the photos app to Dropbox or a similar app after the import using the "send to" feature (I know it works with OneDrive and Google Drive).