hey 

yes you can get seat in karnataka private college without being the domicile if you clear 15% all india quota cut off. see there are two types of cut off. one is 85% state quota which means college has 85% seats for karnataka domicile student. other one is 15% all india quota which means college has 15% seats for students from other state. college will release out their cut off for both quota once neet results are out. if you not karnataka domicile then you will have to apply for 15% quota. 

do ask for more queries. 

thankyou. goodluck.