Going by the trends that we have come across in recent years, any non-Keralite has to secure a rank under 2000 in order to get shortlisted.
There might be a case that a particular branch has performed exceptionally well and even a rank below 2000 doesn’t seem to help. In that case, you have to wait for upcoming lists.
The worst-case would be, you might have to wait for all the admissions to get over for “on the spot admission”. This aims at filling up the left-out seats. But this is just a fluke. It would be better if you don’t depend entirely on this and keep looking for other options at the same time.