The answer to this depends on exactly how you envision this database. At the beginning of the question, it seems that you are proposing monitoring people based on their genetic inclinations. I would not accept this. At the end of the question, however, you seem to be suggesting a database that keeps track of those who have actually committed a large number of crimes. This would be more acceptable, though I do not know that it would be very useful.
It would be completely unacceptable to monitor people because they might be inclined to commit crimes. This is totally contrary to our idea that people are innocent unless they have been proven guilty.
However, if you want to have a database of people who have committed more than a certain number of crimes, there is not constitutional problem with that. This could be written into law and implemented. I do not think, though, that it would be very useful. It might help a few people who, for example, live right next to a person who constantly burglarizes houses. However, if that person were simply to go a little way away from his home, people would surely not recognize him. This sort of a system would be somewhat unfair to criminals who were trying to reform and it would not do much good. Therefore, I would tend to oppose it.