the answer will vary with each individual MP. You will have to do the check for each MP. Based on what I have seen so far, most of the MPs made for SCOM 2016 do not support OS versions prior to Windows Server 2008 R2. An example is the AD MP. The old version of the MP is supported on SCOM 2012 R2 (but not SCOM 2016) and supports older OS versions (2003, 2008), but the new AD MP, which is supported for SCOM 2016, does not offer support for Windows Server 2003 and 2008.
You an check the MP for each component you are interested in and then verify the requirements for it:
Thanks Stoyan. I’m finding the agent is quite unstable on Win 2008 SP2 (Win 2008 R2 is ok)
Official word from MS: https://technet.microsoft.com/en-us/system-center-docs/om/plan/system-requirements
The following versions of Windows operating system are supported for the Microsoft Monitoring Agent connecting to Operations Manager.
Windows Server 2016, Windows Server 2016 Nano Server, Windows 10, Windows 8 Enterprise, Windows 8 Pro, Windows Embedded POSReady 2009, Windows Embedded Standard 7 Service Pack 1, Windows Server 2008 R2, Windows Server 2008 Service Pack 2, Windows Server 2012, Windows XP Professional 64-Bit Edition (Itanium), Windows XP Service Pack 2, Windows XP Service Pack 3.