Yes, it's one of the reasons that the location of objects protruding from the fuselage, ahead of the engine intakes, needs to be carefully considered for aircraft permitted to acrete ice (I can feel a HC vs NL thread developing
)
e.g. mirrors, probes etc
Potentially more severe is slushy ice which can collect on the intakes and then be sucked in, resulting in flame out. I know of two AS332ls that have had double engine flame outs: one over a deck in the hover, the other in the cruise at 5000 ft (he relit before they reached the surface!) I also know of a S-76 (early A model) that had a flame out on take off as ice slid off the intake into the compressor.