Yes it does, if you read the definition.

I guess you can't read. Want me to do that for you too? I'm already doing all the thinking here anyway...

In politics (and particularly in international politics), soft power is the ability to co-opt rather than coerce (contrast hard power).

Brand marketing obviously falls under this definition. For further reading, I suggest the link on the wikipedia page, "Fraser, Matthew (2005). Weapons of Mass Distraction: Soft Power and American Empire, St. Martin's Press. Analysis is focused on the pop culture aspect of soft power, such as movies, television, pop music, Disneyland, and American fast-food brands including Coca-Cola and McDonald's." -- a title that supports my inclusion. I'm sure he could explain it better than me, but don't take my word or wikipedia's for it?

Anything else?

If you had bothered to any reading, there's also this:

The first attempt to measure soft power through a composite index was created and published by the Institute for Government and the media company Monocle in 2010.[17] The IfG-Monocle Soft Power Index combined a range of statistical metrics and subjective panel scores to measure the soft power resources of 26 countries. The metrics were organized according to a framework of five sub-indices including culture, diplomacy, education, business/innovation, and government. The index is said to measure the soft power resources of countries, and does not translate directly into ability influence. Monocle has published an annual Soft Power Survey since then. As of 2016/17, the list is calculated using around 50 factors that indicate the use of soft power, including the number of cultural missions (primarily language schools), Olympic medals, the quality of a country's architecture and business brands.[18]