IDLE should run and calltips and tests should work even callables lack docstrings, either because none is defined or because there are suppressed (CPython compile switch for builtins, CPython runtime switch for user objects).  I believe calltips work with or without docstrings present, but:

One User class test is skipped with -OO.  It should be changed to still work.

Multiple builtin tests fail.  #37501 proposes to skip them when compiled without docstrings.  The right long-term solution for IDLE is to change the tests.  My idea is to expand tiptest with 'out' replaced by the signature part, the processed docstring part, and the docstring object.  I want to try something like 

def tiptest(obj, docobj, sig, doc):
    out = sig += doc if docobj.__doc__ is not None else ''
    self.assertEqual(get_spec(obj), out)