Yes, this will work, but you need to do some studies. There are two manuals, which you need to read. Start with the diagram in the "StudioLive_Series_III_AVB_Networking_Guide_EN_11092018" in section 5.2.1 (page 38). The diagram shows a real complex network and what you want to do is shown in there. The "StudioLive_Series_III_Stagebox_Mode_Addendum_V5_EN_25032019" will give you some basic information.
A real great source of information are the Technical Articles in the "Learn" section of the PreSonus web site. All articles about AVB can be found via this link: https://www.presonus.com/learn/technical-articles/avb-networking.