Answer:
Yes, geographically speaking, Palau(Belau) is in the Micronesian Archipelago therefore making it part of Micronesia. However, politically, the Republic of Palau is a sovereign country under the "Compact of Free Association" with the United States of America and is independent of the politically unified island states of Yap, Chuuk, Pohnpei, and Kosrae that comprise the Federated States of Micronesia also commonly referred to politically as, yes you guessed it, "Micronesia".
So maybe a better answer is, "Palau, and the Marshalls(RMI) for that matter, are in Micronesia and is debate-able depending upon who you ask and what mood they are in".
So as the Micronesian saying goes, in one form or another, "....the ocean does not separate us, but rather, ties us together."