Anyway, my question is: Say I pass the tests, would the "normal" progression be to apprentice for an AI?
There are a few variables to what is normal. You could get on with an airline (121 or 135 operator) and never hear of, or have a need for, the term AI, or IA, ever again. Yes, there are apprentice programs out there, few and far between. I'm sure many A&P's go the route of working at an FBO that have IA on staff, technically not an apprentice, but you do have to work within the bounds of FARs.
65.81 General privileges and limitations.
(a) A certificated mechanic may perform or supervise the maintenance, preventive maintenance or alteration of an aircraft or appliance, or a part thereof, for which he is rated (but excluding major repairs to, and major alterations of, propellers, and any repair to, or alteration of, instruments), and may perform additional duties in accordance with §§65.85, 65.87, and 65.95. However, he may not supervise the maintenance, preventive maintenance, or alteration of, or approve and return to service, any aircraft or appliance, or part thereof, for which he is rated unless he has satisfactorily performed the work concerned at an earlier date. If he has not so performed that work at an earlier date, he may show his ability to do it by performing it to the satisfaction of the Administrator or under the direct supervision of a certificated and appropriately rated mechanic, or a certificated repairman, who has had previous experience in the specific operation concerned.
(b) A certificated mechanic may not exercise the privileges of his certificate and rating unless he understands the current instructions of the manufacturer, and the maintenance manuals, for the specific operation concerned.