If you just want 1password to manage your nextcloud passwords, yes, they can do it. 1password provides browser extensions (and os apps) to auto-fill usernames and passwords into websites for you. It works for many websites, and it should work for nextcloud too.
As for syncing, 1password uses their own servers to store and sync your passwords, Dropbox or nextcloud or other cloud storage is not required for 1password to function. If 1password provides a way to make exports and backup, then yes, these exported files can be synced with nextcloud like any other files.
Just in case, if you’re syncing a certain program settings file/folder of 1password and it works with Dropbox, then it should also work with nextcloud. But then this is probably not a supported use of 1password.
Personally, I use bitwarden as a password manager, and it has been autofilling credentials on nextcloud as it has been on other websites.
Since you’d know best about your needs and requirements, it would be a good idea to test everything you want to do with nextcloud and 1password with the free 1-hour demo of nextcloud