In theory, it should. But it would be interesting to see what DEVONthink To Go itself claims to use and what iOS claims it would be using.
On the iPhone, as yet, the iPhone storage has not come down, with DEVONthink still at 66 GB on a DEVONthink to Go set up that is On Demand only. I have about 7% of unused storage space, and to date I have had no obvious problems in using the device, so as @rmschne has recommended, I won’t bother pursuing this further.
The good news is that I have now repaired both my iPads. The way I did this was to delete all databases and reload them from scratch. This worked.
Clearly, on three devices (one iPhone and two iPads), the installation process went awry, with databases not transferring from v3 to v4 as the installation instructions indicated. For some reason, certain files came across to DTTG4 from DTTG3, and others didn’t. Subsequently, it was not possible to sync any of the databases. My final solution, as I indicated, was to delete all the databases and reload them from scratch.
I have one more iPad to go, which I will be tackling later in the week when I have access to it. My planned approach is to start by deleting DEVONthink To Go 3 on that device and all associated files, and to install DEVONthink To Go version 4 as a new app and load the databases from scratch. I think this would be the best approach, given my experience to date, which has been time-consuming, to put it mildly.
Thanks to all contributors for the help along the way.