Yes, you can create multiple auto responders that go to the same email list categories over several days. There is no logic built into the drip campaign, however. It will send the scheduled messages to all the subscribers, regardless of whether they opened or clicked on any items in previous messages.
For example, you could send a welcome message 1 day after they subscribe, then send information about upcoming events 5 days after they subscribe, and finally send an heartwarming story of your organization's community impact 14 days after subscribing. Each message is unique and has different images, links, and information to inform and invite your new subscribers to become more involved.