Oh yes you can. Recall a previously save configuration from a setup file on the card, and you end up in whatever mode you were when you saved the file. Regardless of where you were when you ordered the recall.
I think we're talking about different things, likely because I was reading more into the posts than was there.
I was referring to the fact that it is not possible to change the mode associated with a C# setting (e.g., change C2 from Av to M) leaving all the other settings intact. Instead, you have to start from the new mode, recreate all the settings, then overwrite the previous C# setting.
No, it isn't. That's a legacy thing. When the first camera with custom modes was introduced (the 40D in 2007), there was no quick control screen. Thus there was no other way to select an exposure mode than by turning the mode dial. Since the custom modes also were located on the same dial, it was for physical reasons impossible to select a mode from inside a custom location, since you had to leave that custom location to access the mode you wanted.
Now, when we also have the custom control screen, accessible via the Q button, it would be technically possible to use that screen to change the mode as well. At least when inside a custom memory location. All current cameras except the 1DX prohibits this when outside a custom mode, since then you again have to physically rotate a dial to select the mode. I can understand that Canon for the sake of consistency have kept the same limitation also inside a custom mode. Doing the opposite would probably have rendered even more calls to the support lines.
Now the 1DX doesn't have any mode dial, and does already today allow you to change mode without even using the MODE button, as it's possible to reload a saved configuration from a file on the card. But, again probably for consisteny (I don't know - I work with product development, but not at Canon), you can still not change the mode via the quick control screen, and thus it's not possible inside a custom memory location either, since they are all selected through the MODE button and then rotating the main dial.
Recently, Canon has shown that the fact that other manufacturers are chewing on their market shares have introduced a more relaxed attitude towards moving outside their traditional bounds of design, so maybe they could give up this constraint on popular request as well. But it will then probably be for the 1DX only. It's technically possible to allow it on the Cx settings only, but I doubt they'll do that on a camera where it will be impossible on all other mode settings, due to the constraints imposed by the physical mode dial.
Thing is, it's about time to leave behind these legacy restrictions and use today's possibilities for user interface design and customisation. I was also negatively surprised by this not being possible on the 1DX. And I don't understand why I can't freely configure ANY function to ANY button, with some macro/script-capabilities added on top! Imagine if all the functions of the camera where available inside a Lua interpreter, and you could assign any Lua-script to any button! If they gave me the source I'd hack that together in no time :-) At least if the original firmware is in C...
I wouldn't say that loading a saved configuration from a card is 'changing the mode'. Yes, the saved mode is loaded, along with all the other settings. That's been possible on several previous 1-series bodies.
There are many features that Canon *could* implement. This is one that, while nice to have, I haven't heard a real clamor for it. Contrast that with EC in M mode with Auto ISO, which has been a popular request for years, and which Canon finally delivered with the 1D X v2 firmware.
There's a somewhat related feature that doesn't seem to be included yet, exposure lock in M mode. That should be pretty easy to add, too, in particular since the AE button doesn't have any other job in M mode.
(To make it clear what this is about, some cameras (but not from Canon) do the following in M mode: when you press AE-lock it acts as exposure lock, so when you then change the aperture the camera automatically changes the exposure time to compensate (and keep the same exposure), and vice versa when you change the exposure time.)
I shoot manual almost all the time and I tend to adjust shutter speed and/or f-stop as a means of exposure compensation. The wheels are placed so that you can use your right thumb and index finger to adjust on-the-fly very quickly. I tend not to use auto ISO because I am frequently adding or subtracting 1 or more stops from the meter reading based on what I am shooting. With birds it is frequently adding 1-2 stops of light by adjusting shutter speed or f-stop or both. If I find the shutter speed is too slow then I increase the ISO (which also can be done with index finger and thumb while still looking through the viewfinder).
Since I have become used to fully manual and can adjust things quickly as it is now I don't know if I would use AE lock in manual mode. It seems like it would be a combination of both shutter and aperture priority modes, or a fully automatic mode once you set the exposure.