They would lose, because the ANO overrides the AICs.
IO540, I agree that the 'IMC DH/MDH minima' paragraph in the AIP (not AIC!) is ambiguous and that there's a very persuasive case for arguing that none of it is mandatory.
But that is
not because the ANO overrides the AIP. AD 1.1.2 (which includes the paragraph in dispute) of the AIP provides the notified method of calculating minima as specified by Articles 48 and 49 of the ANO, and as such is mandated by the ANO.