I would seek permission before messaging customers. WA messages are like text messages. I find it intrusive to be sent an unsolicited message from any business unless I registered or accepted their terms of communication.
Also, if not handled well, you may actually lose customers if the frequency of messaging is not right, ie 2 messages an hour is not ok or 5 messages a day. I suggest do a pilot with say 10 customers. get an insight into how they react to them. A market survey and see how they respond.
One thing though is lack of privacy with WA groups. Your personal number and profile is open ****** to everyone in the group. Not sure how people may react to that scenario!