Depends on your age and situation.
If you are not legally an adult (so under 18) and they are told you are likely to harm yourself they will start looking for you very quickly.
In short the younger you are and the more serious harm you can/are likely to do to yourself then the more seriously they will take the situation ,the quicker they will start searching and the more intense the search will be.
If you are legally an adult (aged 18 +) then you have a right to 'disappear' (people do just vanish and go make a life for themselves somewhere new without telling anyone they know. It happens.) and go wherever/ do what you like/not contact anyone you don't want to. Now , if someone cares about you and goes to the police then the police will listen and make out a standard 'Missing Person Report' but not do much else at all.
But if they are told you are likely to hurt or kill yourself then , even as an adult ,that is a bit different and then they will try to find you.
The trick then , if you want to go through with it , is to make sure they can't.