I would like to send an alarm to a list of people one at a time and only notify the next person on the list if the first person did not reply. Is this possible?

Yes. This feature is called the Alarm profile.
You will need to set up a set of CSV files under the offline project Alarm folder and then publish it.
You can set up multiple profiles for different days and times. Containing a specific list of destinations for each profile.
Each profile contains a list of email addresses and phone numbers that the system will call and wait for a response. If no ACK or Rest response comes back, it will proceed to the next call.