Is it mandatory to go missed following full scale CDI deflection?
The point being, once you've reached a full scale deviation in IMC, there's no telling how much beyond it the airplane has gone. Your USA AIM 5-5-5 is quoted here, and point 'b' is sufficient to conclude an immediate Missed Approach:

5-5-5. Missed Approach
a. Pilot.
1. Executes a missed approach when one of the following conditions exist:

(b) Determines that a safe approach or landing is not possible.


With a full scale deviation and the LOC beam narrowing as you approach the RWY, what is the pilot going to steer at low altitude and descending lower in IMC? What is the IFR reference that the pilot would use? A VOR course? An FMC course? A locator beacon (NDB)? Even if these existed, there would have to be an IFR procedure to continue to landing, including revised minimums.
Quoted below are the Elements of a Stabilised Approach, widely accepted as The Gospel by regulators and industry, All manufacturers have incorporated into their procedures, this concept from the Flight Safety Foundation's ALAR 'toolkit':
(ALAR = Approach and Landing Accident Reduction )
(notice too, the applicability to VMC conditions)


Most airlines and other aviation organisations specify minimum acceptable criteria for the continuation of an approach to land. These vary in detail but the following summary published by the Flight Safety Foundation is one view of the important considerations.




Their Approach-and-landing Accident Reduction (ALAR) Briefing Note 7-1 suggests that &quot;all flights must be stabilised by 1000 feet above airport elevation in IMC and 500 feet above airport elevation in VMC. An approach is stabilised when all of the following criteria are met:





The aircraft is on the correct flight path
Only small changes in heading/pitch are necessary to maintain the correct flight path
The airspeed is not more than VREF + 20kts indicated speed and not less than VREF
The aircraft is in the correct landing configuration
Sink rate is no greater than 1000 feet/minute; if an approach requires a sink rate greater than 1000 feet/minute a special briefing should be conducted
Power setting is appropriate for the aircraft configuration and is not below the minimum power for the approach as defined by the operating manual
All briefings and checklists have been conducted
Specific types of approach are stabilized if they also fulfil the following:
ILS approaches must be flown within one dot of the glide-slope and localizer
a Category II or III approach must be flown within the expanded localizer band
during a circling approach wings should be level on final when the aircraft reaches 300 feet above airport elevation; and,
Unique approach conditions or abnormal conditions requiring a deviation from the above elements of a stabilized approach require a special briefing.




An approach that becomes unstabilised below 1000 feet above airport elevation in IMC or 500 feet above airport elevation in VMC requires an immediate go-around.