Would Microsoft Office 2016 work in Monterey OS?

Your best recommendation is to forget about Office 2016 and only use the current Microsoft 365, Office 2019 for Mac, or Office 2021 for Mac Office suites as they are currently designed, and supported with product updates for Monterey.

Office 2016 for Mac was developed years ago, and retired by Microsoft before Big Sur or Monterey were released. What are the odds that the 64-bit version of Office 2016 would work without issues on Monterey without Microsoft testing and revising that Office suite code for Monterey?

You would not be able to complete a new installation of Office 2016 for Mac on Monterey as Microsoft has disabled their license servers for their retired products, so entering a product code would bork.

I have no issue using Office 2016 on my MBA M1 with Monterey even though no more MS support.

Current-patched 2016 will probably work.

Microsoft did the 32- to 64-bit transition necessary for Catalina and newer via patch (15.25 and later) within the lifetime of 2016.

https://docs.microsoft.com/en-us/office/troubleshoot/office-for-mac/office-2016-for-mac-64-bit-upgrade

But Office 2016 is also two versions back, and is very much unsupported. So load it, and if it breaks, roll in your pre-upgrade backups and revert, or acquire a newer Office or an alternative.

Other users here have posted that Office 2016 does NOT work with Monterey