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Absolutely.
Here are a couple of informative threads with things to look out for: 1 and 2.

If installing from dvd or cd the autorun probably will not execute, so you will need to use windows explorer to navigate to the setup program on the DVD and run it manually.

Also, best to install to a directory named c:\games instead of the default c:\programfiles. See the links above for why that is so.
 
To add to what Red Jacket said.

Install a clean version of Doomsday.
Install Armageddon into the Doomsday folder
Apply the 1.2 Armageddon patch into the Doomsday/Armageddon folder.

If you have the Anthology then Armageddon is a stand alone game.

Install Arma
Apply the 1.2 patch to Arma. Make sure the installer directs it to Paradox Interactive/Armageddon not Paradox Interactive/Doomsday/Armageddon