Ahh! The light goes on. Yes, you should be able to do that- the insert points will allow you to split the channel right down the middle, and use the preamps and the mix busses entirely separately.
By using an insert cable (a Y cable, 1/4" TRS-to-2x1/4" TS), you can hook the output side of the insert cable to the inputs on your soundcard, and the return side of the insert to the outputs on your sound card. The tip on the TRS plug will be the send to the soundcard, and the ring will be the return from the soundcard.
The preamps and gain trim controls will be on the send side, and will act on the mic signals going out the send and into your soundcard inputs. The EQ, faders, and aux bus sends will be on the return side, and will act on the signals coming _out_ of the soundcard. That'll let you get 4 busses worth of mixing: one stereo pair and the two mono auxes. So realistically you can get 3 somewhat independent monitor mixes out of the unit. You only get _somewhat_ independent mixes, because the Aux2 send is post-fader: so changes to the mix on the main stereo pair will affect it.
The bad news here is that there is no zero-latency bypass path created by the mixer when you monitor this way (splitting the inserts entirely): all the outputs to your mix busses are by definition coming from the soundcard, which means that any latency inherent to those outputs will be present on your monitor mix. Now, I don't know a dadgum thing about the 1010: perhaps it has a zero-latency hardware monitoring path, in which case that last point is moot. But if the gozintas have to go through the A/D and D/A conversion with a buffer or two in the middle before they get to the comesoutas, the outputs you'll get will be delayed, and you may find that latency to be a problem in monitoring.
If that happens, you'll need to do the good old single-click insert steal for your mic preamps to the soundcard inputs (so that you can monitor with zero latency), and then repatch the soundcard outputs to the insert or line ins to do a final mix with the 12R . The real question is "does the 1010 have a zero-latency hardware monitoring mode?". If the answer is yes, you're in fat city...
Hope that helps.