'storage almost full' message - still backed up?

For the last few months I've been getting the message that my iCloud storage is full and that my iPhone cannot be backed up. Despite deleting a number of photos, apps, music etc, the message continued to appear and I couldn't back up my phone.

Now, for some reason my phone is broken and I need to restore. Obviously I panicked as I thought I had no backup, however I remember noticing that in the last week the message had changed to 'Storage almost full' rather than 'iPhone cannot be backed up'. Does this mean I the phone was most likely backed up recently, if the message has changed to 'storage almost full'?

Thanks