1. As per sec 80GG they have clearly mentioned as "not being an assessee having any income falling within clause (13A) of section 10" if we go by this definition then sec 80GG cannot be claimed irrespective of receipt of HRA or not.
2. But the overall point in the introduction of sec 80GG is to give benefit to the person who is paying rent and at the same time not in receipt of HRA.
3. Prudently speaking sec 80GG should be available for the month in which the employee is not in receipt of HRA. But it is not wise to show both HRA and as well as sec 80GG in the return together as it will gain attention from the department.
4. But from a provision angle, it should not be a problem. If ITR allows for you to claim HRA and sec 80GG at the same time, file the return and if the department raises any query on the same you could give an explanation. Provided rent-related documents are available.
Please correct me if the above interpretation has an alternative view.