Not really. For Dropbox, Nextcloud, Photo Sync, et c to upload your photos, the app needs to remain open; it can't upload in the background for more than a minute or so.

This means that only iCloud can do real background syncing. If you want to upload a full camera roll to a non-iCloud service, you're in for a world of frustration. You'll have to disable screenlock and put the phone on a power cord and leave it open with the app up for hours and hours. Of course iCloud doesn't have such limitations.

No non-Apple app is allowed to do background sync, no matter what you install. They have put iCloud Drive and iCloud Photos in a privileged position.