Whats the current file IO on the servers in-prem hosting this data?
Now imagine that being shoved back and forth thru your firewall to the cloud.
Yes, One Drive can be configured for local caches, copies etc. but sounds like a mission to hell, at least at first.
How do they propose to do the migration?
Big Bang? [Switch off friday, Transfer TBs over the weekend and all users are go on Monday]
Phased implementation? [Groups of users moved across]
Side by side / parallel run? [Old fileshares and OneDrive coexist]
And before they go whacking all this data in the cloud, what controls are being put around it? I believe One Drive [for Business] allows you to share docs, directories etc with people outside the organisation.
Great for collaboration. Nightmare for Data Protection.
Also consider "Are you allowed to store all this in the cloud". You may have contracts with organisations which prohibit it. I know we do (we're looking at this too, and fortunately for me, I'm NOT involved in it

). You'd be amazed what financial clients say you can't do with their data [regardless of what they themselves do with their own data!]