There may be some possibilities here, although without a 970 in hand I can only theorize. Basically, though, I believe that this is possible with the proper wiring.
The DVI output is purely a DVI pass-through, so to have both DVI output and s-video monitor output active at once you'd need to have both DVI and s-video signals connected to that specific input. Likewise, if your source is component video, you won't get any composite or s-video monitor output unless you also have a composite or s-video signal connected (since the 970 doesn't transcode down from component to s-video and composite). That means that to have an s-video cable run to your little LCD monitor and have it getting a signal no matter what input is active, you'd need to make sure that you have a composite or s-video cable run from each video source - even if the source in question is using a component or DVI connection to the 970 for the signal going to the main display. This matches very nicely with the video signal path description on page 16 of the 970's manual, so what I describe should work!