According to MSI CPU SUPPORT LIST for your motherboard it does support it.: https://www.msi.com/Motherboard/support/MPG-B550-GAMING-PLUS#support-cpu
But you will need BIOS Version 7C56v17.zip installed for the motherboard and BIOS to recognize and boot up with that processor.
But you will need to check to see if the RAM Memory you have installed will be compatible with the new processor by looking at the same link above under QVL List for RX5xxx for RAM MEMORY: https://www.msi.com/Motherboard/support/MPG-B550-GAMING-PLUS#support-mem-21
Or simply if you have the correct BIOS Version installed, just install the new processor and see if it boots up without any issues if the RAM is not listed in the QVL List.
Now you want to know if you might need a BIOS update or if it will work out of the box depends on the date your motherboard was manufactured.
BIOS Version 7C56v17.zip is the latest version for that motherboard model which came out on 06/28/2021. So if your motherboard you purchased was manufactured after 07/01/2021 then the processor should work out of the box since it will have the latest BIOS installed but if you received an older manufactured Motherboard made before 06/28/2021 then you will probably need to do a BIOS update on it.
NOTE: Just go to whatever Motherboard you are planning on buying and check under Support its CPU SUPPORT LIST and RAM MEMORY QVL LIST and then go to BIOS download page and check to see what date the oldest BIOS version will support your new Processor.
EDIT: Just noticed that your motherboard has a BIOS FLASHBACK feature on it. So it doesn't matter when the motherboard was manufactured since all you need is a Flash drive with the latest BIOS version to update the BIOS even without a processor installed. Just need to apply power to the motherboard and press the BIOS FLASHBACK button with the Flash drive installed on the special USB BIOS FLASHBACK port.