Hi Sherry
Yes, the site mailboxes don't show up in the Exchange Admin Center but they can be dealt with through PowerShell pretty much the same way as other mailboxes. The cmdlets to hide/delete them are the same as for any other mailbox and I've mentioned them in some of the comments earlier in this thread.
Hi James
When you remove the mailbox you essentially delete the mailbox with all its content. Hiding from GAL just makes the mailbox non discoverable. So take the step that you think is suitable for you. I don't think I can give a definitive answer on how long the command will take to reflect since that could be a function of a number of things. But if hiding from GAL doesn't work as expected then feel free to raise a ticket. Also do let me know if were able to get your script to work. If you weren't, I could point you to someone who could help you out with it.