How accurate is the WORD COUNT in OOWriter?

Short answer is that for simple documents without section headers or chapters or references, then yes it's perfectly accurate. For documents with those things, or if you're not counting words of 3 letters or less (as some people seem to prefer) or if you have other non-standard requirements for the word count, then no it's not accurate.

Long answer, it depends on whether you want to count words of three characters or less. Some people when writing papers or articles don't count words of three letters or less, or the words in section/chapter names, towards the final word count. In that case, then no it's not accurate. Also, if you have a reference (such as "To be or not to be, that is the question (Shakespeare)") the word count will be higher because of the reference.

However, if you want to know exactly how many words are in the document counting absolutely every word, then yes it's accurate.