Is it safe to throw exceptions from within C++ noexcept functions if you want to terminate the program?

Question

Passing an exception through a noexcept function is supposed to terminate the program. My question is whether it is safe and reasonable practice to rely on this behavior in cases where you could have a program bug that leads the exception to be thrown.

A simple example would be when you want to call the same functions on both validated and unvalidated input, as in here:

#include <stdexcept>

struct tree {};

tree
parse(char *p)
{
  if (*p)
    throw std::length_error("only 0-length arguments allowed");
  return {};
}

struct validated {
  char *buf_;
  validated(char *buf) : buf_(buf) { parse(buf_); }
};

tree
parse(const validated &v) noexcept
{
  return parse(v.buf_);
}

In the above code, I would like parse(const validated &v) to be noexcept. Of course, there could be a bug in the code where I modify a buffer after it has already been validated. In that case I would like the program to crash and dump core like an assertion failure, but I want to avoid the risk of undefined or otherwise exploitable behavior that could do worse than crash the program.