Deploying MSI via group policies

no, just wait some time or force manual refresh with gpupdate /force in a cmd window.

You can do a gpupdate /force and then it should install during the boot/Windows startup process (before the logon screen appears).

GPO software installs *Only* take place during the startup process.

So yes you will need to reboot

can I do a automatic install without rebooting using a batch file:

msiexec.exe \\xyz.com\gpo$\Inventory\TEST.msi /qn /norestart

Put it in the GPO, and this will push out automatically to all the servers I have in an OU, without user intervention and server reboots?

Would you be using the .bat as a logon script ?

Do users have admin rights ?

Do I need more than this?
Yes Administrative rights, etc.

msiexec.exe \\xyz.com\gpo$\Inventory\TEST.msi /qn /norestart

It has to be done via PowerShell Script, so I was able to do the MSIE command which I have to embed into PS.

msiexec /i "\\xyz.com\gpo$\TestInventory\Test Inventory.msi" /quiet /norestart
That worked when I tried it @ the command line.

Now I have to put that into a PowerShell script which I have as:

$script = {
   
$args = "/i "\\xyz.com\gpo$\TestInventory\Test Inventory.msi"  /quiet /norestart
[diagnostics.process]::start("msiexec.exe", $args).WaitForExit()
   
}

I am going to try this script and see if it works from Power Shell ISE