Basically yes. In finance this is considered to be pretty normal AFAIK. Maybe not directly sending them a message immediately after adding them, but in general

Basically yes. In finance this is considered to be pretty normal AFAIK. Maybe not directly sending them a message immediately after adding them, but in general people try to add other people from big shops(Goldman, MS, UBS, big hedge funds, market makers,etc.) and then once they want to start exploring a move it isn't really that uncommon to be able to reach out. If you announce yourself that you are leaving a company and looking for something new you might not even have to go looking yourself.