I've answered my own question, by purchasing and testing a Compute Module 4 and I/O board.
It would appear that the Linx toolkit does indeed target a Compute Module without any apparent problems.
The only two issues I had were :
1. The USB ports are disabled by default, so they need to be enabled :
[To enable the USB 2.0 ports on the Compute Module 4, you need to edit the boot config file (/boot/config.txt) and add:
dtoverlay=dwc2,dr_mode=host]
2. There was an error when trying to deploy from the Linx toolkit :
LMH-LINX.lvlib:Local IO.lvlib:Load Device Channels.vi loaded with errors on the target and was closed.
To rectify :
go to this directory
" /svr/chroot/labview/usr/lib "
and change name of "liblinxdevice_RPI2.so" to" liblinxdevice.so".
After that, everything seems to work fine.