Thickeners of any type are used to keep the pigment suspended and to prevent sag while thinning sufficiently to allow for easy mixing and good flow. The ammonium acrylates can be used in place of CMC and HEC thickeners but the term 'ammonium acrylate' is not a sufficient descriptor to give you any specific information. These acrylates are usually available as a copolymer specifically manufactured for specific applications. The exact nature of the copolymer is usually proprietary in nature. If you are modifying an existing formulation, the compatibility of each of the ingredients with the acrylic will have to be determined.
No one knows the advantages and limitations of these materials better than the manufacturer so perhaps you should start there. BF Goodrich (search Carbapol), Rohm-Haas (search Acrysol), Archem (search Arcosperse).