I wish we could have a cadet program around here! They keep trying to get it to work but unfortunately you need clinical time in the ER before you can complete the local emt class. Non of the hospitals locally will let you do your clinical unless you are 18 and older.....
As far as having a student or less trained emt on the ambulance, my agency does it! But is has to be a crew of 3, 2 experienced emts and 1 student/noob. If they are a student, they can only do basic First Aid skills and the field report. If they are a noob, we start them off slow and easy, starting with vital signs, field report, Basic FA and then as time goes on and they prove themselves more they get to do more stuff! It is a great way to get knowledge and experiance..... Just dive in and learn all the hands on stuff you can (with close supervision of corse)!