It is not necessary to base a position on this question on the usefulness of any given code construct or practice, nor on anything written about C++, whether in its standard or in another SO answer, no matter how similar C++'s definitions may be. The key thing to consider is C's definition of undefined behavior:
behavior, upon use of a nonportable or erroneous program construct or
of erroneous data, for which this International Standard imposes no
requirements
(C2011, 3.4.3/1; emphasis added)
Thus, undefined behavior is triggered temporally ("upon use" of a construct or data), not by mere presence.* It is convenient that this is consistent for undefined behavior arising from data and that arising from program constructs; the standard need not have been consistent there. And as another answer describes, this "upon use" definition is a good design choice, as it allows programs to avoid executing undefined behaviors associated with erroneous data.
On the other hand, if a program does execute undefined behavior then it follows from the standard's definition that the whole behavior of the program is undefined. This consequent undefinedness is a more general kind arising from the fact that the UB associated directly with the erroneous data or construct could, in principle, include altering the behavior of other parts of the program, even retroactively (or apparently so). There are of course extra-lingual limitations on what could happen -- so no, nasal demons will not actually be making any appearances -- but those are not necessarily as strong as one might suppose.
* Caveat: some program constructs are used at translation time. These produce UB in program translation, with the result that every execution of the program has wholly-undefined behavior. For a somewhat stupid example, if your program source does not end with an unescaped newline then the program's behavior is completely undefined (see C2011, 5.1.1.2/1, point 2).