Looks like I was wrong.
I put my iPad into Airplane mode, and browsed my iCloud Drive. I checked a lot of files, and only found one that was not stored locally, but that's enough to prove I was wrong. I'm guessing iCloud Drive does like many other iCloud services do, and only keeps the files local that it thinks you're likely to use. How many files probalby depends on how much storage you have on the iPad. I have the 256GB iPad Pro, so I'm unlikley to see this limitation often.
There is nothing I can think go that will change this behavior for iCloud Drive (if it is intentional behavior and not the result of some other overlooked issue on my part.)
If you must use iCloud drive for this, the only work arround I can think of is to tap and preview each of the files on iCloud Drive while you have a wi-if connection. Provided you are not running low on iPad storage, they will probably stay local for quite a while afterwards.
Otherwise I suggest using another cloud storage solution. You could use Dropbox, but it requires you to identify each file you want to stay local. That would be nearly as awkward as having to tap on individual files in iCloud Drive. Doable with a few files, but quickly unmanageable when the numbers grow.
Box.com is another popular cloud storage service with a free tier. It's more complicated to use than DropBox, but you can specify entire folders to sync locally; along with a lot of other sharing controls.
Google Drive will allow you to keep folders local as well. You 'star' them. I haven't used Google Drive for this, so I can't say how well it works.
In all of these cases you will need to open the apps on the iPad now and then to make sure they stay synced.