I've never done it, but I see no reason why it wouldn't work.
The amp portion of the ARII runs off of nominally "10.3VDC", which is in reality often about 12VDC. It should be quite happy to operate on 12V from a switcher.
A couple of minor points to keep in mind:
1) the ARII has no volume control, you'd need to provide any volume control seperately (either on the input, or the output side)
2) if you are amplifiying two independant channels, you may not be able to achieve the same maximum power that most Atari games could. This is because they most often had mono sound, with two out-of-phase versions of the same signal on each side of the amp, and connected the speaker across them ("bridged mode"). Using each TDA2002 seperately, you'll have half of the total power for each channel. In a home environment, you likely won't be operating near max volume, so this probably won't be a concern.