In C99 there're some (optional) types like int8_t, int16_t and the like, which are guaranteed to be have exactly specified width and no padding bits, and represent numbers in two's complement (7.18.1.1). In 6.2.6.2 signed integer overflow is mentioned as footnotes 44) and 45), namely that it might result in trapping values in padding bits.
As intN_t don't have any padding bits, and they are guaranteed to be two's complement, does this mean that their overflow doesn't generate any undefined behavior? What would be the result of e.g. overflowing multiplication? What about addition? Is the result reduced modulo 2^N as for unsigned types?
Footnotes are not normative. If a footnote states that overflow can result in trapping values in padding bits, it is not really wrong, but I can see how it is slightly misleading. The normative text merely says the behaviour is undefined. Placing trapping values in padding bits is one possible consequence of undefined behaviour, but not the only one.
So no, this does not mean overflow is defined. It's possible for operations involving intN_t/uintN_t operands to overflow, and for that overflow to result in undefined behaviour.
Something like int8_t i = 127; ++i; has no UB. int8_t is subject to integral promotions, so the addition is carried out as if you had written i = (int8_t) ((int) i + 1);. The addition itself does not overflow, and the conversion back to int8_t produces an implementation-defined result.
Something like uint16_t u = 65535; u *= u; has UB on current typical implementations where int has 32 sign/value bits. uint16_t too is subject to integral promotions, so the multiplication is carried out as if you had written u = (uint16_t) ((int) u * (int) u);. The multiplication itself overflows, and the behaviour is undefined.
Something like int64_t i = 9223372036854775807; ++i; has UB on almost all implementations. The addition itself overflows.
No, it isn't well defined because ... it isn't defined at all. There simply is no text in the standard that would give semantic to the overflow of a signed integer.
Don't overstress the term "undefined behavior" as being something mysterious, but take in its direct sense. There is no definition of the behavior, so the standard doesn't specify anything what should happen and no portable code should rely on such a feature.