I don't want to use Apple's Mail.app on macOS - Any unintended consequences? Mail app is using 10GB on my laptop (High Sierra 10.13.3). I don't use it at all; I usually use the web interface and occasionally Thunderbird for my Gmail account. 

This is the only Mail-connected account in Internet Accounts. If I were to uncheck it in Internet Accounts for my Gmail account so that I can delete the cache and free up some space, is there the possibility of any unintended consequences? For example, will I somehow stop getting email reminders of things in my BusyCal calendar? Or some other possibility that I am unaware of?
It is safe to remove your Gmail account from Mail.app without any unintended consequences, as all the Gmail data is stored on Google's servers.

Also, there’s no harm in never setting up any mail account in Mail.app for macOS. The system does want to have a default mail app, so if you click a mailto://hi@me.com link, it will open Mail.app. Mail will then try to onboard a new account, but you can end that action easily by not choosing to continue.

Simply removing a Gmail account from Mail.app won't delete any of your Gmail data (although performing any action on any of the mail or folder will reflect the changes in Gmail). This is the same for any purely cloud based IMAP mail services (iCloud as well as Gmail) where deleting the local cache leaves the server copies of all mail intact.

The only small caution is if you save mails locally and delete a copy from the server - maybe make a quick backup of your Mac or export your local mails to an export file or folder just in case you fear you’ll delete those and want them back.