Chris got it right, if my measurements are to be believed: there's a change in timbre, but not power.
Several years ago I got interested in the discussion about break angle. Folks would post on (mostly steel string) lists on line to say that they had increased the break angle over the saddle and the sound improved. When I asked them how they'd changed it, usually they'd say it was by putting in a taller saddle. Since this alters both the break angle and the string height off the top, I did an experiment to see which of the two variables was having the biggest impact.
I set up a 'test mule' classical guitar with an 18-hole tie block. This allowed for tying the strings in two ways: the usual one into the holes in front of the block, or by passing the string over the tie block and into the holes in the back. The usual tie gave a break angle of about 25 degrees, while the modified tie gave a minimal break of around 6 degrees. I also made a taller saddle so that the 'back' tie would give a 25 degree break. The regular saddle put the strings 11 mm off the top, while the tall saddle had them at 18 mm off the top (don't try this at home!).
I used a mechanical plucker based on the 'wire break' method to get uniform plucks of the open strings for each setup case. The sound was recorded on my computer using a microphone one meter out in front of the guitar in a 'semi-anechoic' closet. I compared six plucks on each string to make sure they were reasonably uniform. I also made up a 'synthetic strum' for each case to use in listening tests. These were randomly paired and played back through ear phones. Listeners were asked only if the sounds were 'the same' or 'different'.
Objective measurements showed that there was no significant difference in the maximum amplitude, or rise or fall time, for the plucks in any case: the overall power output of the guitar was the same as far as could be told. There was also no difference in the spectral content of the sound for the two cases where the string height off the top was 11mm: changing the break angle does not seem to alter the amount of sound the strings can put into the top. Raising the string height to 18 mm off the top resulted in two changes in the sound output:
1) there was more energy in the second partial, and, in some cases, in the fourth partial of the string, and
2) there was more energy at the frequency of the longitudinal 'zip tone'; a compression wave within the string that is normally up around the 7th or 8th partial.
String tension rises twice per cycle at it vibrates, and this pulls the top of the saddle toward the nut, rocking the bridge at even multiples of the fundamental pitch and producing some top motion. The longitudinal 'zip tone' wave acts in much the same way. A taller saddle gives both of these signals more leverage to produce sound. Presumably, energy fed into the system in this way reduces the power available to drive the bridge through the more effective 'transverse' force, which may explain why there's no more power available with the taller saddle.
In the listening tests people were basically guessing when they were called on to compare the two 'low' saddle cases with different break angles. Virtually everybody heard the difference between the 'low' and 'high' saddle cases. Thus it seems that the measured differences in harmonic content of the sound between the cases translated pretty reliably into perception.
Although I did not ask for impressions of timbre, it does seem as though the increase in output at the 'zip tone' pitch could well be perceived as a 'sharper' or 'more cutting' timbre. It comes in at relatively high frequencies, and is usually more or less dissonant, so it would tend to stand out .
Sorry for the long post, but I wanted to get a summary of the work out.