Good day meelamri,
Yes. You could force "Not Allow duplicate" for whole organization users while not for whole instance entity.
It depends on your duplicate detection rule like you don't want Account with the same account name or same mail address.

If you haven't created any detection rules on any entity & its related field. The 'Allow Duplicate' window wouldn't be popped out like following example:
I have enabled duplicate detection while have no rule on case entity. So when I create one case with the same name under the customer. There's no more warning after I created it.

Above info is also mentioned in Doc:
To determine whether a record is a potential duplicate, Dynamics 365 for Customer Engagement apps uses duplicate detection rules. When publishing a duplicate detection rule, a matchcode is created for each existing record. A matchcode is also created when a record is created or updated. When a record is in the process of being created or updated, its matchcode can be checked automatically against the matchcodes of existing records. By default, Dynamics 365 for Customer Engagement apps has simple duplicate detection rules for accounts, contacts, and leads. For example, you detect duplicates by matching the record fields, such as email address, first name, and last name.
https://docs.microsoft.com/en-us/dynamics365/customer-engagement/admin/detect-duplicate-data
Hope above info could help.
Regards
Johnny