Will a six speed shifter in friction mode work on either or both sides of a 3x7? SIS Shimano indexed 6 speed. Using an RSX triple set up in place of 6 speed.

Sure, I've used 6-speed 105 shifters in friction mode over a 7-speed cassette. The overall width isn't too different.

How about the front, going from double to triple? Enough cable pull?

If we're talking downtube or bar-end shifters, I think it was always the same front shifter whether you had a double or triple.

Is the FD a triple derailleur? Most of the nonspecific Shimano FD's I've tried do not have enough in/out travel to shift a triple. The lone exception is the FD6207 600 series. Maybe the RX will as well.

Yes, its an RSX set from a touring rig so it should work

Shimano made triple specific front derailers..... for sure in the RSX100 series and in others.

The front RX100 shifter on my old Cannondale R500 is labeled "Triple", and I found when I converted the bike to a double chainring, with an RX100 double FD, the lever only travels about half as much as other levers designed for doubles. SO, clearly a lever for a triple will have more cable pull. Whether the shifter for a double has enough pull, I can't say.

Right, front derailleurs would/should be different... I was just thinking of the shifters.

Time-consuming. I moved a 2x6 Centurion Lemans RS (yellow/black), to 3x7 using a Shimano RXS 3x7 group pilfered from a Diamondback Expert TG. The RXS triple crankset was 110BCD and used the double BB with no issues.

I've done countless double to triple swaps with both DT and stem friction shifters and never had to change the shifter. I've also gone from a 5 to 8 speed on the rear without changing the friction shifters. I'm not sure how much travel the 6 speed Index shifter has in friction mode, mine are all packed away, but it should at least be enough to handle an extra cog.

3 or 4 years ago Shimano 3 X 7 indexed DT shifters were cheap and plentiful on Ebay, I see that is no longer the case.