After searching the web I did not find much on importing a fixlet to a site using the REST API and cURL. Is this even possible?
It is possible, yes
For reference, please see the POST method described here: https://developer.bigfix.com/rest-api/api/fixlet.html
As for an example with cURL, please see https://developer.bigfix.com/rest-api/examples/create-fixlet.html