Is there a way to run a word count that doesn't include LaTeX commands?

You can run a word count via the Project menu:

Word Count button in the Project menu

This will run the texcount utility to count the words in the project's main file and any files that are included / inputted into the main file. This will include references. If you do not want to include references in your word count, you can comment out the \bibliography (or similar) line and re-run the word count without the references section rendered. We are working on an update to provide an option to include references or not - we hope to have this soon.

The word counts exclude latex commands and are broken down by context. Words in headers and figure captions are counted separately, which is helpful if the word counting rules you need to follow stipulate that certain words be included or excluded. Here's an example of the output for a simple document:

Example output from TeXcount

We're running the texcount utility using the following flags: -quiet -merge -incbib -dir -sub=none -utf8 -sum.