Will the "World Wide Web Publishing Service" be stopped while the StoreFront "Propagate Changes" is in progress?
Yes. During "Propagate Changes", the "World Wide Web Publishing Service" on the destination StoreFront server is stopped and started.
*World Wide Web Publishing Service will not be restarted on the source StoreFront server.
Troubleshooting StoreFront propagation issues
https://support.citrix.com/article/CTX206872/troubleshooting-storefront-propagation-issues