How can I use (parts of) a managed account without submitting my device to the Device Policy?
He would have to use the web interface via a browser in order to access this account. Adding the account would make it subject to the administrative policy, and this they would be able to monitor and erase his device.

Now, the real question is why would they bother? I can tell you with a fair amount of certainty that no one is sitting there monitoring accounts with their fingers posed over the WIPE button, they don't have time or care and these features are generally never used unless the circumstances are fairly significant, bad enough for a school administrator to be willing to take the heat from a pi$$ed off parent and be able to justify their actions. 

These feature are usually employed at the enterprise level, where a person leaves a position, to make sure the company's data is wiped from the device and they do not take it else where, or to be able to locate or clean the device should be it be misplaced/stolen. The ability to "monitor" the phone is somewhat over-rated, as they can't go in and read your text messages or see what calls your making to who, it simply means they can monitor data related to the account that has device administrator access. The problem is these are kind of all in one permissions, for your child to be able to access this account the ENTIRE permission applies. 

The answer is although this is a possibility, the concern is likely unfounded. You should be able to allow your child to add his school account to his device with no issue, and when that account is no longer needed the administration rights can be removed and the account with it.