Yes, it will index perfectly. So long as you match the shifters and FD with the correct indexing standard, the shifter controls the indexing.
Your 10 speed road shifters and your 9 speed MTB RD both use Shimano's legacy "SIS" cable pull standard, so you're good to go.
I've built bikes with 10-speed 105 ST-5700 brifters and 9 speed XT RD-m772, and the same RD with 10-speed BS79 bar-ends.
Just make sure you have a ST-5703 left shifter and FD-5703 front derailleur, for your triple crankset.