tuning a convolution neural net, sample size
If you use pre-trained weights, you need significantly lesser data as the initial layers have already learned from a ton of data and you just need to fine tune the later ones. 

What you said is not true, you can train on CIFAR10 and get 90%+ and that is not 100k+. It depends on the complexity of the data and how similar the features are. If they are easily Seperable -less data. If the disctintions are harder then the model needs a lot of examples to figure out which of features are seperate. 

I would say you could IF you sample was representive of the population.