will DA downtube shifters...

[eddief]

shift a triple front derailleur?

[dbrk]

Yes, both the 7800 and 7700 DA dt shifters will work with a triple front. And even Shimano agrees! (Lots of stuff works that Shimano says doesn't, of course.)

dbrk

[christian]

Yes. I have 7700 DA d/t shifters shifting a TA Zephyr 48-36-24 with an XT M751 front derailleur on one bike.

- Christian

[Louis]

It's friction - friction will shift nearly anything.

[Ray]

It's friction - friction will shift nearly anything.
If it has the range. I did have a set of Shimano DT shifters once (I think they were 8 speed) that wouldn't shift a triple with any front derailure I could find. Most do though.

-Ray