Yes, this is the best idea to compile them in an email sequence so that new subscribers can get your previous broadcasts. When you create an email sequence, you would decide the flow of that sequence using rules or filters; You can do this using Automations. You can determine who would receive the emails you would like to send. I would recommend you look into these links and the other relevant automation links.
The tutorial above would show you all the possibilities you can work with to make sure the emails are sent to those only you would want them to.