I don't think it's outwith the realms of possibility that it could have. The squad is poor, but barring the Dundee United victory, the other QFs showed how good/jobby the other teams left are.
Looking at it conversely, how could you imagine that a squad that had far higher-quality players like Hammell, Lasley, Pearson, Ainsworth, McManus, McDonald and Johnson could almost get us relegated? It took a one-off tie as such for that squad to keep us in the division. Who's to say that the current bunch of dross couldn't have shithoused it's way to the cup?