Yes, private colleges of Karnataka are also included in ALL india counselling. Here are some reputed colleges with their expected cut off (for UR category) in NEET 2020:

(final cut off will be released by KEA)

1. BANGALORE MED. COLLEGE,BANGALORE - 644 marks
2. BELGAUM INST. OF MEDICAL SCI., BELGAUM - 594
3. BIDAR INSTITUTE OF MEDICAL SCI., BIDAR - 588
4. Bowring lady Curzon Medical College Research Institute- 598

Check out the cut off for AIQ in other colleges of Karnataka here:

https://medicine.careers360.com/articles/neet-cutoff-karnataka