There was a discussion on this a few years ago.
http://festoolownersgroup.com/ask-festool/correct-storage-for-cms-modules/
Given the "CMS and Basis module tower MT 1600" is designed for "space-saving storage of the CMS and Basis modules", if you look at the dimensions, it has to have been designed to have tools attached, but I can't find any official recommendation. However, given how the modules are supported in the CMS itself (i.e. the insert plate takes all the weight) I can't see that it would cause issues.
I understand the plates are quick thick, and are ribbed to prevent deflection, so I can't see that leaving a tool attached would do much harm.
When my new kit arrives, I'm planning to leave the TS 75 permanently attached unless I need something more than the TS 55 as a mobile tool. Not so sure about the OF 1400, and for the PS 420, I've bought a spare guide mount and vacuum adaptor so that I can just clip the Carvex on and off.
The Festool tower supports the modules on their long edge, so I'd plan to copy that if at all possible. I've seen other designs supporting the short edges, but I always try to assume that Festool has it's reasons for doing things the way it does...
It's also shown in some Festool literature that you can leave the Festool routers attached, fold the legs, and still place the whole unit in the back of your van, so again, I'm assuming it's OK for them to stay in the modules.
So bottom line is I can't find anything to say you positively can, but I also can't find any evidence to say it is a bad idea, and although only the belt sander and Carvex modules are in the photo, at least the Carvex is still attached [source: Festool web site]
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