Context: We have multiple Business Admins in different countries, who can only see records from their market in Salesforce. Now, we're considering giving these Business Admins access to the Developer Console by checking the API Enabled checkbox on their profile.
Question: Does enabling the Developer Console (by checking API Enabled) mean users can write Apex/queries that affects records they normally can't see in Salesforce?
Update: Just for future reference: It turned out that if you're a System Administrator and you login as another user, you still see the Developer Console in the menu. If you login as another user directly though, it's not there and Bradley's answer is where you should look for more information.