I have background app refresh setting turned on for DTP to go on my iPad however unlike Evernote on the iPad it does not refresh in the background but I typically have to wait a couple of minutes for it to sync with iCloudkit before I can use it. Evernote is always in sync so no delays. Maybe I am doing something wrong as I would have though having background refresh turned on would keep it in sync automatically and ready to use as soon as you open up the app.
Background App Refresh is controlled by iOS, not the application. It allows it when it allows it and terminates a process when it sees fit.
PS: There’s no way to verify Evernote’s behavior as the syncing is not the same and the amount of data typically being passed is also not the same.