Yep it will, just fine.
Some, like the SLX double have a 'tighter' curve on the cage to deal with the smaller 22/36 type rings. Many, like the SRAM offerings, and the new XTR ones don't.
I've used plenty of 2x9 bikes with a triple (and a road double) front mech with no ill effects, always with reasonably large rings though (no smaller than 28/42).
On the 2x10 groups the cable pull is optimised to work with double front mechs, but I've heard numerous people saying triple ones work (not tried it myself).
So... long story short is that a triple one will be fine, 10 speed double one may be slightly smoother.