Theres a bit of a mis understanding here.
Selected precision approach? As in get vectors to an ILS and fly the approach? Thats the normal situation. You can manage NAV to a waypoint on the extended center line, then arm the LOC and GS. Youll nav to the intercept point, then pick up loc. You can sort of call that Managed but its not really. Youre just in NAV to a waypoint instead of a vector.
Managed and non managed refers to non precision approaches. Ie NDB, LOC only RNAV and VOR. In this respect, doing them managed or selected is down the the SOPs of the company and what the crew decide on the day. Managed reduces workload. Selected is no harm as you need to be able to do them in case a managed mode fails for whatever reason. Theyre always flown with autopilot in or else youre into raw data.
Getting vectors to intercept an ILS which is autopilot flown is the norm.
Managed non precision is when the autopilot takes care of the lateral and vertal guidance. AP will keep you in the profile while you monitor the height checks and tracking.
Selected is when you decide the vertical with V/S or FPA. Lateral is controlled by Heading or Track. You will not stay on the profile and will constantly have to modify selections as you are only following a radial and are not locked on to anything.
In terms of what you said about only being able to do a managed approach only if youre cleared for an approach. Doesnt really make sense, ATC wont have a clue if youre managed or selected. Or care either. Once you are cleared for the APP you fly the approach in whatever way you had planned.
Think your understanding of what these modes mean is a bit off the mark or what is done day to day. Hope this helps