No, I do not know it or precisely how to calculate it.
To be called low "Q" I think that the number has to be around 2-3, but certainly not 6, 8, 10 or more.
The formula for calculating Q is the frequency divided by the bandwidth. That's fairly easy in a non-chirp transducer if you have access to the beamplots and certain graphs. Not so readily done on a chirp transducer but there are some indicators. Since the Q involves dividing the frequency by the bandwidth the wider the bandwidth the lower the resulting calculation. The bandwidth is readily available.
For example. The Airmar B75L spec sheets say it has a Q of 2. It's bandwidth is 40-75. That's a range of 35. See the attached pic from airmar. Pay particular attention to the peak performance range. That's what you don't see on non-chirp transducers. Now look at the P66. On 200 kHz they give it a Q of 37. Now look at the graph. The peak performance has very little range. The graphs for Figure of Merit may be more applicable but both illustrate the point that chirp transducers peak performance is over a range of frequencies and non-chirp transducers peak at a very narrow range. That range is a critical number in the Q calculation.
The GT52 range is 150-240 on the 2d element. That's a range of 90. That is a really wide range. Again, I don't know how the formula works here for choosing what frequency to use in the calculation but if it was 200, then 200/90 which would be just over 2. Worst case scenario would be 240/90 which is 2.67. Best case scenario would be 150/90 which is 1.67. So for any Garmin chirp transducer you could reasonably accurately calculate both the best case and worst case possibilities. So it is safe to say the GT52 is a low Q transducer.
Another point. I have not found that Garmin, Lowrance, or Humminbird misrepresent their products when publishing technical information. Sometimes you have to read closely what they say like Hbird cone angles measured at -10db instead of -3db that most everybody else uses. So 20 degrees Hbird is not the same as 20 degrees Lowrance, but it's still 20 degrees, the way they define it.
Having used the GT8, GT50, GT51, and GT52 I am quite confident that they are all low "Q". The test is to use them on a manual frequency setting at both ends of their range and see that the performance is still really good.
Sometimes we hear of a transducer having a "sweet spot", meaning a singular manual frequency that seems to do better than other settings, such as GT50 on 105 kHz. If we had the full technical specs, beamplots and graphs, you would be able to identify that by looking at that data.