Doug,
I think that would be an interesting experiment to try right here at my home course. I've played it at least 50 times or so, so i have a pretty good history on what I normally shoot. I could go out and play a Sunday afternoon round where instead of teeing off on every hole I take it 250-260 yards off the tee and put it in the fairway somewhere...and then play in from there.
It would be interesting to see what I shot in those conditions over a few rounds.
As for my 1st shots that finish on the green, consider the following two scenarios:
1) I hit the green in regulation which I usually do 4-6 times per round. As I rarely end up within 20 feet of the pin as I'm a higher capper, at worst its about 30% longer from 20 feet to 26 feet. For my average approach at 30-40 feet from the pin, adding 6 feet to the putting distance only makes the putts 20 to 12% longer...which is almost negligble. I still two putt these and every now and then run one in for birdie.
2) I miss the green and have a chip of 30 yards or less to the pin. Sure every now and then I'll chip one in nice and close for a gimmie putt, but in total, I'd put my "up and down" % at maybe 10% tops. So assuming I have 10 holes per round like this, I'm only losing 1 stroke because instead of that two foot tap in, I now have an 8 footer which I probably only make 20% of the time. On all the rest of my chips, I have a 16 footer instead of a 10 footer, or a 21 footer instead of a 15 footer. I still two putt those putts all day long, every day....so no increase in strokes there.
Now sure you could say that I need to improve my chipping game, and you would be right. But consider this...the best players in the world can only manage to do this 55% of the time. As a higher capper, I could work my butt off and maybe get to 25%...but that's still best case scenario. So even if I improved from my current estimated 10% to 20%, that still only saves me on average 1 stroke per round.
Hence my money saves I can improve far more quickly and effectively by improving my long game to have approaches from 140 yards in the fairway as opposed to 195 yards away in the rough....which I would estimate at 4-6 strokes per round.