I'm sure someone here knows more about this than me.
But what I've gathered from working with modern LCDs is that they present an essentially capacitive load. So yes you can put a DC source onto them and they will charge like any capacitive load and generate a static field between the common electrode and the segment electrode. In between of course you have the liquid crystal which is electrochemically twisted in the presence of this field.
The problem is that the LC doesn't like to see a permanent (DC) field - this can lead to eventual (electrochemical) breakdown of the carefully aligned LC and so deterioration of the display. As noted in my initial reply, short term DC signals are unlikely to damage the display but neither would I spend a lot of time driving them with DC, particualrly with an aged component. So there's obviously nothing dodgy with the recommendations in the service manuals you cite but you would never design the actual equipment to drive with DC over the long term.
The drive signal to LC segments is usually chosen to be high enough to avoid the static fields that lead to LC degradation, high enough not to have visible flicker and low enough that you don't have trouble driving the capacitive load. In the hundreds of Hz is typical and I've never seen anything over 1kHz. Most LC displays these days incorporate all of the switching drivers into a module so you can just drop DC control signals onto them but if you're designing with glass only (as I think most vintage LC watches) then the ouput control signals will (almost always) be AC/switching.
The problem with not having a QC input to the display driver IC in your watch would be that the outputs to the LC are (almost certainly) designed to be AC/switching waveforms and by removing the clock then the output circuits won't be functioning properly. Which particular voltage they latch to if powered up without a clock is anyones guess but the two most likely states are either high-Z or 0V. Some or all could latch to a non-zero voltage sufficient to switch on a segment but there are many implementations that simply wouldn't. I would be interested to hear from others whether they've had any dark/dim/random segments on dead Xtal vintage LCs - always interesting to work out how they designed these circuits way back when (well for some people anyway
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In an LED watch the output drivers are (most usually) going to be current sources with fixed regulation and a simple on/off input from the logic circuits. This means that when the IC is powered up without a clock and enters whichever mysterious state the logic circuits drop into then a coherent unclocked output is often produced to switch on (latched because the IC logic is unclocked and static) one or more current sources and so LED digits.
I think the answer to your intial question is the same. And the service manuals are also right. Hopefully I've explained why? Or possibly sent you to sleep.
Anythings possible but some things are more likely than others.......