Josh,
That's an interesting possibility but maybe in the opposite direction. I play the shorter tees (more or less "senior" tees) most of the time and the Par 3's are quite short (100-160 yards). So actually I may have more than my share of putts inside 15 or 20 feet on the Par 3's.
As you can see from this breakdown, relative to Tour players I am pitiful in the 6-10 foot range. That's my putting weak point and maybe the very shortest Par 3's where I'm hitting a wedge or 8/9 iron are giving me "too many" eight-footers (just joking, I'll take all the eight-foot birdie putts I can get!).
2, 3, 4, 5 feet Strokes Gained Putting= -0.11536765
6, 7, 8, 9 feet Strokes Gained Putting= -0.25416667
10, 12, 15 feet Strokes Gained Putting= -0.16378049
20, 25, 30 feet Strokes Gained Putting= -0.16227273
35 feet or longer Strokes Gained Putting= -0.14900000
Of course Strokes Gained does not account for any possibility that for a given distance I may be leaving myself above the hole more often or something like that. But that sort of thing should average out over 100+ holes.