Pretty much as the title says, do messages in archive count to your total inbox space?
Yes, messages that are archived count towards your storage quota.
Even messages in the trash and spam are counted. The only difference is that messages in the spam and trash will probably be permanently deleted within 30 days, which automatically frees up space in your account.
Your storage use is based on the size of all of the messages and attachments in your mail, including those in Spam and Trash.