Hypothetically you can, but I've heard of a lot of people having issues with mountain front derailleurs and getting the indexing "just so" with STI levers.

Now if you're using a bar end, which is friction, it doesn't even matter.

Basically all of this crap kind of sucks, and shifters are expensive. I'm going 1x9 with a kelly take-off on my cross bike this season, I think. KISS.