If you go through File | Properties and choose the Statistics tab, you get a word count, but it omits all of the footnotes (or endnotes). As far as I can see, there is no way to customize it to make it count the notes.
There is, of course, an alternative:
There is another way to get a wordcount, which is to go through Tools | Word Count, and this has the stupid behavior as its default: it will omit footnotes and endnotes unless you check a box.
Although checking that box makes the latter wordcount include the notes, this makes it incompatible with the other way of getting a wordcount, so that the two give different numbers.
It’s a sad day when the premier (supposedly) word processor is more concerned with the process than with the words.