Have you seen the new Office 365 on Horizon operational tutorial? https://techzone.vmware.com/resource/best-practices-delivering-microsoft-office-365-vmware-horizon-7-0
It's got some detailed info about making OneDrive work with non-persistent desktops, which is a requirement for App Volumes. Specifically, making sure you're using the latest OneDrive Sync App (rather than the older groove.exe, for example) and installing Office components with shared computer activation (necessary for non-persistent desktops) may help.
We have tested OneDrive successfully on 2.18.2 with Writable Volumes and it works with no issues. We do have one fix for a specific issue regarding OneDrive in 2.18.2 where an online file is not accessible the first time it is accessed.
Please see the VMware App Volumes 2.18.2 Release Notes for more details.