How to set a default value to a Word Cloud

I would like to set a default value of either “All” or “NA” on a Word Cloud until the value changes by using an action. I can limit the Word Cloud to show only 1 value but cannot find a way to specify that value.

One way to do it is to use conditional rendering to choose which Word Cloud to use: word cloud with single “All” word or the read Word Cloud.
See Conditional rules - Amazon QuickSight for more details

To generate a word cloud with a single word, just add a constant calculated column to the dataset (with expression “All”)

Is it possible to use this functionality with an action rather than a control?

Yes. Conditional rendering relies on parameter value.
You are able to change parameter value in the navigation action

See more on actions here: Creating and editing custom actions in Amazon QuickSight - Amazon QuickSight