You should have mentioned the same in your CV as well. If the employer is not okay with it, they will reject your application, and the question of joining and subsequent background verification will not arise.
On the other hand, if you have received the appointment order, then the background verification will be done for the documents related to experience only. Moreover, distance learning is also a degree awarded by a university and is on par with any regular degree.
Of course, some companies prefer candidates with degrees from reputable colleges or B-Schools. However, such companies will clearly state in their employment criteria the requirement for degrees from top-tier colleges.