Yes, I've successfully recorded 4 channels out of my Involve V1, Tate II, CD-4 demod, and Q8 deck using the Behringer unit and AA3.
Here's what you need to do:
1. Open AA3 and create 4 mono tracks (insert -> audio track or Alt-A).
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My copy of AA3 seems to open with 6 tracks by default - to delete tracks, simply right click and you'll get a pop-up menu with "delete" as one of the options.
2. Save your session (File -> Save Session As). Once you start recording, AA3 will output the 4 .wavs in a folder in the location you've selected.
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3. Go into "Audio Hardware Setup" (click the input box on any of the tracks, shown in the first picture), then click "Multitrack View" and select "UMC ASIO Driver". You should see 4 mono outputs, like in the picture below.
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4. Assign the proper inputs to each track and arm them to record (click the "R" box in the top left corner of each track)
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Once this is all set, you can simply hit space and begin recording.