This isn't a guarantee from the standard, but as another data point, v.push_back(v[0]) is safe for LLVM's libc++.
libc++'s std::vector::push_back calls __push_back_slow_path when it needs to reallocate memory:
void __push_back_slow_path(_Up& __x) {
  allocator_type& __a = this->__alloc();
  __split_buffer<value_type, allocator_type&> __v(__recommend(size() + 1), 
                                                  size(), 
                                                  __a);
  // Note that we construct a copy of __x before deallocating
  // the existing storage or moving existing elements.
  __alloc_traits::construct(__a, 
                            _VSTD::__to_raw_pointer(__v.__end_), 
                            _VSTD::forward<_Up>(__x));
  __v.__end_++;
  // Moving existing elements happens here:
  __swap_out_circular_buffer(__v);
  // When __v goes out of scope, __x will be invalid.
}