Just for fun, and because I like math, I computed the equilibrium of a simplified game. I gave blue 2 strategies: "hit" or "run away" with the colo, and I gave red 2 strategies "bluff with cap" or "chase with gen". In poker terms: blue has "fold" or "call", red has "bluff" or "value bet".
For better or worse, I took piece value from Vincent de Boer's thesis. This has the rough guideline that (with the high ranks still on the board) rank R is worth the same as rank R-1 + R-3 combined (marsh ~ gen + major), slightly more than 2 pieces of R-2 (marsh >= 2 colos) and about the same as 3 pieces of rank R (marsh ~ 3 majors). Info on piece of rank R is worth about a R-3 piece (major for marsh info, cap for gen info). So I took as points an unkown gen = 90, known gen = 62, known colo = 42, unknown cap = 29, sarge = 14.
Then I plugged these strategies and payoffs into the open source tool Gambit.
The equilibrium is for red to come out with the cap 25% of the time, and 75% of the time with a gen. For blue, the equilibrium is to run away 75% of the time, and to hit 25% of the time. The net value for red is less than 4 points (about a 1/4 of a sergeant).
So if you can convincingly represent the chasing piece as a gen (in this case, it came from D3, so it was believable) this mixed strategy is a slightly +EV gamble. If you only do this 25% of the time with a cap, you are indifferent whether blue calls or folds with his colo.
I ran the same analysis for chasing a known gen with either a major or a marsh (either unknown) when there is a captain present for the major to pick up if it doesn't get hit. In this case, there is also a small +EV gamble to bluff a major 22% of the time, and for the gen to call this 33% of the time. The EV is about 1/4 a captain here, not a very high reward for such a risk.
Conclusion: regardless whether these numbers are 100% accurate, in cases where you have a mid-level piece on a believable general starting place, you can make a very small gain (about 1/4 of the time you succeed in gaining the sergeant) by sometimes bluff-chasing the colo, for a pretty big risk (a captain down, vs a known colo up minus gen info).