To answer the original question, yes you can lose weight while on TRT but this weight loss will be driven by your diet not by your mileage specifically or exercise generally. The weight gain associated with TRT is from an increase in water retention due to the bolus of testosterone delivered by periodic shots as well as the increase in lean mass. It is not my experience that TRT in and of itself is effective for weight loss. So, when you combine water retention with an increase in lean mass with no corresponding decrease in fat mass you have a resulting overall significant increase in weight.
is it possible that TRT was a contributing factor in your calf strain? I would say the probability is greater than 0 though not necessarily due to the gain in weight but instead the increase in intra-facia pressures caused by edema secondary to water retention in the lower legs. Crippling calf pumps are a well-known phenomena among lifters who take supra-physiological doses of testosterone. It's possible that something similar happens when TRT is combined with the constant stimulation of running.