Multiple accounts on one device, in conjunction with Pokemon Go Plus and Adventure Sync

No

... because you can't be logged into two accounts on the same phone. You can store multiple Google accounts, but only one can be logged in; active at a time per device.

Adventure Sync credits distance to the account currently logged in and Go Plus is tied to the device, which in turn is tied to whichever account is currently logged in.

Your best bet is to get two phones, which lets you Adventure Sync for both accounts but you obviously can't connect a Go Plus to two phones at the same time because of how Bluetooth works.

TLDR: Both accounts would need to be logged in at once. If you don't need the additional benefits of PoGo Plus (catching and spinning), just take both phones with you and use adventure sync.

No this would not work. Here are a few of the issues you will have:

Go Plus Connectivity

The Pokemon Go Plus device (according to people who have it) only stays connected for about an hour at the time before needing to be reconnected. In addition to this, it is pretty annoying that it vibrates every time there is a Pokemon/stop to spin and generally is pretty noisy and hands on. For your purposes, it would not work because of the fact that it is communicating to the app on your phone to track your distance and while your phone is locked, you cannot have multiple instances of Pokemon GO running (to the best of my knowledge).

Multiple instances of PoGo

This is only possible with an Android device which has some applications that allow you to run multiple instances of applications at once. This, in theory, would allow you to run multiple instances of PoGo at once with different accounts. The issue with this is I do not think it will keep those instances open while not using the app.

Proposed Solution

Since you already have two devices for raid hours and events, you may as well use them both while you're walking. To make things easier on yourself, you can get a Pokemon Go Plus and weigh the button down with a coin and some tape to auto spin and catch while you walk for one account. If you are only looking for adventure sync benefits, you can just walk with both phones.