For a pointer p, could p < p+1 be false in an extreme case?

Is it possible, for a pointer variable p, that p<(p+1) is false?

If p points to a valid object (that is, one created according to the C++ object model) of the correct type, then no. p+1 will point to the memory location after that object, and will always compare greater than p.

Otherwise, the behaviour of both the arithmetic and the comparison are undefined, so the result could be true, false, or a suffusion of yellow.

If yes, under which circumstances can this happen?

It might, or might not, happen with

p = reinterpret_cast<char*>(numeric_limits<uintptr_t>::max);

If pointer arithmetic works like unsigned integer arithmetic, then this might cause a numeric overflow such that p+1 has the value zero, and compares less than p. Or it might do something else.