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Yes, very possible. You can have multiple sound cards (or more generically, audio interfaces) active and working and making sound at the same time.
Windows can only have one sound card active as the default audio device. The default audio device will get system sounds and be the default choice for audio applications that are only able to play to the default device. So that means apps like iTunes, Windows Media Player, Flash (YouTube, your browser), many games, etc. will all play over the
default audio device and won't be able to be played over whatever is set as a secondary (non-default) audio device.
Smart applications like Foobar, J River, professional level audio editing apps, etc. will have an option that will allow you to select that the app play to a particular audio device. So an app like Foobar can play to any audio device that is connected to the computer.
Use the "Sound" applet in Control Panel to select what audio device is the default.