Yes, use something like Nurfed Combatlog or Simple Combatlog and set it to watch your warrior in question. You will see messages come by saying "Warriors gains *** stance". And you can filter to gains with nurfed aswell, so you see what stance a warrior is in without too much spam.
There's no way to get the "hidden aura" of a warrior's stance, unless he's sharing the info thru an addon specifically designed to do that, or unless he actually switches stance(then you see SoandSo gain Battle Stance. in the log). You could code an addon that catches stance specific ablities to find out, but there's no way to tell right away what stance is a warrior in.
If I recall correctly, you could set the combat log to a higher range, and have it report Auras gained/lost by others. Stances are treated like Auras, and (again, if memory serves) you could configure SCT to report that as well. I'm at work so I have no real way of telling this 100%, I'll give it a shot later tonight.