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Exam slots are awarded on a first-come, first-served basis, so it’s definitely possible. Majority of candidates also tend to register around the registration deadlines, so you would also be competing with more candidates for the same slots.
Also, I wanted to know what happens if I have registered for an exam but in the scheduling process, I am not able to find a seat in the test centre of my city. What can I do then?
This is not really clear, and in my opinion a flaw in CFA Institute’s current scheduling setup. Your exam will be voided if you don’t schedule your exam within the given deadline, but yet it is possible to have no exam slots in your chosen location.
If this happens to you, I would suggest trying to seek alternative locations, or otherwise emailing CFA Institute stating you have no available exam slots (info@cfainstitute.org) ASAP.
Good luck, and let us know how it goes!