The thing is that you can't uninstall a preinstalled app like Gmail. The reason to try Safe Mode is to see if some other app you installed is somehow interfering with Gmail's proper function.
Even if you could uninstall the Gmail app, it wouldn't remove your Google account. There are many other apps that use your Google account (like the calendar app, Google Drive, etc.). In order to remove your Google account, you'd have to go to Settings>Accounts, select your Google account, then tap Remove Account.