No, it would not. Compilers can remove boundary checks that provably happen after accessing an item of an array, not those before the array is accessed.

For your example, the Pascal code (at least, I hope this is Pascal; it has been a while since I wrote any):

  if (i>=0 and i<16) then
  begin
    x := a[i]
  end
  else
  begin
    ReportError;
  end

is equivalent to the C code:

  if (i>=0 && i<16)
  {
    if(i>=0 && i<16)
    {
       x = a[i]
    } else {
      RuntimeAbort(“Array access outside bounds");
    }
  } else {
    ReportError();
  }

A good Pascal compiler, like a good C compiler, would optimise away that second boundary check and the call to RuntimeAbort. Neither compiler is allowed to optimise away the first check.