As an on-board player and referee I sometimes (actually, today)
encounter situations like this. White just managed to exchange
queens on b5 (Kb2 Pb5/Kb6 Bd5 or suchlike) but his flag fell.
The FIDE quickplay rules unequivocally say that White loses
on time since he can play on self-mate (yes, I know, help-mate
is the correct term, but all on-board players call it a
self-mate in conversion, even I who knows :-) by promoting
to a knight and further braindead moves. (The rule is idiotic
but sensible - "winning chances" can't be defined properly.
The poor geezer should have thrown a "10-2" beforehand.)
Thus: In case of fallen flag the game is lost *exactly* when
a help-mate can be constructed. Is there any interesting
problem with the stipulation "Is a help-mate possible at all?"