The only way to do this is to gather a large pool of training data, analyse the frequency of cross training pops with and without the gym. This analysis may be impossible as it would likely take thousands of data points to compare all the ages, at all the heights, all the training possibilities (both skill trained and trainer level). It would take much more than simply self reporting in a forum.
That said, I have had 3 cross training pops since I bought a L3 gym. Haven't had one in about 3 or 4 seasons prior to that. May that's just a coincidence, but I like the gym!