That's what they try to do. It helps to have a definitive date to help fix some of the layers in time. Volcanic eruptions deposit ash and high sulfur content in the ice. Counting layers and finding signals from the Krakatoa/Krafla/Tambora/Thera (Santorini) eruptions helps indicate if the layers in the ice are truly annual or not.
Palaeo Environment (Ice Cores)
Paleo Slide Set: Low Latitude Ice Cores: High Resolution Records of Climatic Change and Variability in the Tropics and Subtropics (has a picture of ice core layers)
Yup. They will be careful though because some years could be compressed due to the weight or even melted together due to a slightly warmer period. The ice cores are not as dependable (like tree rings) as a year to year record but, are best at monitoring 'periods'. Some years will be clearly discernable and identifiable as a particular year but, not all years. There will be years missing but the date of those missing years will be known.