Two-State Toggles Should Never be Mandatory
I would say that a Yes/No toggle (or any other two-state toggle: On/Off, A/B etc.) should never be marked as mandatory, whether it is disabled or not.
The reasoning: to me, marking a control as "mandatory" means "you must supply (missing) information here". For fields such as a person's name, or their telephone number, this makes sense. Where a user is asked to "check all options that apply", this makes sense. In the case of a two-state toggle, this does not make sense, since the control is always in one state or the other: there is no "I haven't told you my answer" state. The same ban on being marked as "mandatory" would extend to a standard set of radio buttons where – although there's more than two states – one of them is always selected.
For a "mandatory" flag to make sense to a two-state toggle, or a collection of radio options, you would need to introduce a "not yet chosen" state.
I have seen this done with non-standard radio buttons, where initially none of the options are chosen, and you are not allowed to submit the form while it is in this state. (Once one option has been chosen, they behave like "normal" radio-buttons, and selecting any option deselects the previously selected one). However, I don't recall seeing this done with a two-state toggle (and, given the confusion that sometimes arises in trying to indicate which state a two-state toggle is in, I'd be wary about trying to add a third state).
Other Types of Disabled Control Probably Should be Mandatory
If one of the other types of control is used (one that does have an "answer not supplied" state), but where answers to earlier questions have determined the answer and that that answer cannot be changed, then I probably would continue to mark it as "mandatory" for consistency with times where previous answers had not determined the value.
(Although I suspect the number of cases where this would apply to something more complicated than a two-state toggle are limited: in most cases I can think of, earlier answers might have determined a default value [e.g. Billing Address that defaults to an earlier-entered Shipping Address, but a different address can be used], so in general such controls wouldn't be disabled, and the "mandatory" marker would still be needed.
In General: Don't Hide Unalterable Answers
Moving away slightly from your main question: some people might suggest hiding questions to which an answer is already known, and the user isn't allowed to alter it: presumably on the grounds that if they cannot change anything, there's no point in showing it.
I would take the opposite view: if they cannot change it now (because of answers to earlier questions), but in other circumstances could have made a choice (if earlier answers had been different), then I would show the pre-filled-but-disabled choice. Doing so alerts the user that they might have been able to decide for themselves at this point.
In many cases, it won't matter: the user made their choice earlier, and the consequences of that choice would have been obvious. However, in more complicated cases, all the effects of earlier choices may not have been clear at the time: coming across a pre-filled-but-disabled control may alert the user to a side-effect of an earlier choice that they weren't aware of. They now have the option of shrugging their shoulders and carrying on, or going back and altering their earlier response.