This is an interesting question. I'm an engineer so I'm intrigued by the question.
I recently was mixing a recording and had to match the right and left channels. What I discovered is that in the final mixdown, if I had the right and left matched to within .01 second, then I couldn't hear any noticeable delay effect. If they were .02 seconds or more mismatched, you could hear the difference between the two as reverb. So, let's use .01 sec as our acceptance criteria.
OK, according to wikipedia, sound travels at 343m/s at 20C, dry air. You say that your mics are 10 to 12 meters away from the stage. That means that there is a sound delay from the stage to your mics of 12m / 343m/s...or roughly 0.03 sec (or three times the length of Michael Phelps' fingernails
)
I'd say based on this, that you'd probably have some issues with delay.
However, even if you do have to make a 0.03 second adjustment in post, you only have to do one minor adjustment, since the overall clock of the two sources (SBD and mics) would be the same if you were recording with an R-44. IOW, just shift your mic source 0.03 seconds back on the timeline and your two sources will be perfectly synched for the whole show.
This would still be far easier than synching sources from two separate recorders...and I think worth having a 4 channel recorder for, especially since you only have to babysit one recorder in one location.