No, it doesn't. Please read the Doctrine of Fascism.

sjsu.edu/faculty/wooda/2B-HUM/Readings/The-Doctrine-of-Fascism.pdf

Everything must be for the state and must take part of the state. The nation comes from the state and only accepts those who work within its bounds; nothing can exist outside of it.

Mussolini spells it out in the first few pages.

The Fasces used frequently on older buildings have nothing to do with Fascism itself. It is about law, power and governance.