No, you need to add that logic yourself. For file-based inputs, Splunk keeps track of where to start looking for new events in the file by storing to which position it's already read the file. You need to implement the same kind of thing in your scripted input yourself - find a unique incrementing ID of some kind, then after you've queried the REST webservice store the highest ID and then next time you're querying the webservice compare event ID's against that max ID to make sure you're only getting newer ones.
