For sure, although I should say, for this specific instance I ended up training a network from scratch. I did get inspiration from the MobileNets architecture, but I did not keep any of the weights from their ImageNet training. That was shockingly affordable to do even on my very limited setup, and the results were better than what I could do with a retraining (mostly has to do with how finicky small networks can be when it comes to retraining).
I guess the interpretation is that the first few normalize->convolution->pool->dropout layers are basically achieving something broadly analogous to the initial feature extraction steps that used to be the mainstay in this area (PCA/ICA, HOG, SIFT/SURF, etc.), and are reasonably problem-independent.