If you set up the phone to back up automatically to iCloud, you would have seen constant messages about backups not being able to run.....because there was not enough space on iCloud.
Was that still the case up until the time that you forgot the passcode? In the last day or so....before you added more storage on iCloud......did you see a message about backups not being able to run?
If yes, automatic backups were already enabled, so the new backup might run, but you will have to wait a day or two to find out if the complete backup of your phone actually completed by logging on to iCloud from your computer or another device to check the size of the backup file.
However, if you turned off automatic iCloud backups to stop the messages about not enough storage space, then there is no way for you to turn automatic backups back on, since you cannot get into the phone to change the setting.