Not in any well-studied animal; for example, C. elegans certainly has both excitatory and inhibitory neurons. Even in animals with very simple and poorly understood nervous systems (for example, jellyfish) there are certainly inhibitory and excitatory neurotransmitters used, even though one could argue whether their nervous tissue cells are all that similar to neurons of more organized animals.
More broadly speaking, I think it is non-controversial to state that "excitatory" versus "inhibitory" communication between cells predates the development of nervous systems themselves.
Note that neurotransmitters used vary across species, so although glutamate is a common excitatory neurotransmitter in vertebrates, that does not mean glutamate is a common excitatory neurotransmitter in other animals.
Bargmann, C. I. (1998). Neurobiology of the Caenorhabditis elegans genome. Science, 282(5396), 2028-2033.
Martin, S. M., & Spencer, A. N. (1983). Neurotransmitters in coelenterates. Comparative Biochemistry and Physiology Part C: Comparative Pharmacology, 74(1), 1-14.
Kass-Simon, G., & Pierobon, P. (2007). Cnidarian chemical neurotransmission, an updated overview. Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology, 146(1), 9-25.