Thank you for the opportunity to help you with your question!
Yes, a database can contain two identical records. Structure of the database/table decides whether identical records impose negative effect on the integrity. If database table don't have any defined key or other 'unique' constraints, then we can have multiple identical records while opposite is not true. Although it is not a recommended practice in design of database.
Please let me know if you need any clarification. I'm always happy to answer your questions.