Can I transfer everything I have stored on my phone to iCloud storage?
No - not directly, iCloud is not general purpose storage like Amazon S3 or Dropbox offers where you can push files to the store and then delete them and transfer back.

Yes - indirectly, you could ensure your iCloud backup holds everything you care about, turn off backups, delete enough things to run the update and then immediately erase all content and settings to restore the entire backup to your device.

There isn't a good way to actually test that your iCloud backup is complete other than restoring it to a new device since you have to erase your primary device to then get to the restore.